Hydration of Lanthanoids(III) and Actinoids(III): An Experimental/Theoretical Saga

The latest experimental and theoretical studies on structural and dynamical properties of lanthanoid(III) and actinoid(III) ions in water have been reviewed. In the last years, most of the issues about lanthanoid(III) hydration have been resolved combining X-ray absorption experiments and different theoretical methods. Since 2008 an effort has been made to treat the entire series thus obtaining coherent sets of experimental and theoretical results that were lately put together in such a way that it was possible to derive new basic properties, such as effective ionic radii, across the series. While for the hydration of lanthanoids(III) many experiments and simulations have been reported, the hydration of actinoids(III) was less investigated. There are some experiments performed by different research groups and few simulations that we discuss in this review. Currently, there are enough results that it is possible to gain some understanding of the hydration behavior of lanthanoids(III) and actinoids(III). The ultimate goal of this review is to provide clues on the analogies and differences between the two series. These aspects are connected to several issues: 1)?technological: the separation of these elements that is necessary for recycling and stocking of nuclear waste, 2)?practical: because experiments on actinoids need particular care, the definition of possible analogies will give the possibility to use the correct lanthanoid when the information on a specific actinoid is needed, 3)?fundamental: related to chemical similarities between the two series.     

Empirical force fields for biologically active divalent metal cations in water

We have presented a strategy for deriving ion-water van der Waals (vdW) parameters that implicitly include the microscopic solvent molecular effects around the ion. The strategy can be used to obtain vdW parameters for metal cations of the same formal charge and known experimental hydration free energies. In this work, it was applied to derive the vdW parameters for 24 divalent metal ions with measured hydration free energies ranging from -300 to -572 kcal/mol, coordination numbers (CNs) from 4 to 15, and ion-O (water) distances from 1.67 to 2.90 angstroms. The strategy used to derive the vdW parameters employs (1) a numerical procedure that links the coupling parameter used in free energy simulations with the experimental hydration free energies and (2) the first-shell CNs and structure for the entire series of divalent cations. One of the parameter sets obtained (referred to as MWc) simultaneously reproduces the observed (i) relative hydration free energies, (ii) first-shell CNs, and (iii) average ion-water distances of all the dications studied. In particular, the MWc parameters reproduce the observed (i) decrease in the CN from 6 for Cu2+ to 4 for Be2+, (ii) no change in the CN of 6 for dications with hydration free energies between those of Cu2+ and Cd2+, and (iii) an expansion of the CN from 6 for Cd2+ to 9.5 for Ba2+. The ion-water parameters derived herein represent a first step in the simulations of metalloproteins, which will also require potential energy functions incorporating polarizability, charge transfer, and other electronic effects to accurately model the protein-metal interactions in aqueous solution.     

Ion-water clusters, bulk medium effects, and ion hydration

Thermochemistry of gas-phase ion-water clusters together with estimates of the hydration free energy of the clusters and the water ligands are used to calculate the hydration free energy of the ion. Often the hydration calculations use a continuum model of the solvent. The primitive quasichemical approximation to the quasichemical theory provides a transparent framework to anchor such efforts. Here we evaluate the approximations inherent in the primitive quasichemical approach and elucidate the different roles of the bulk medium. We find that the bulk medium can stabilize configurations of the cluster that are usually not observed in the gas phase, while also simultaneously lowering the excess chemical potential of the ion. This effect is more pronounced for soft ions. Since the coordination number that minimizes the excess chemical potential of the ion is identified as the optimal or most probable coordination number, for such soft ions the optimum cluster size and the hydration thermodynamics obtained with and without account of the bulk medium on the ion-water clustering reaction can be different. The ideas presented in this work are expected to be relevant to experimental studies that translate thermochemistry of ion-water clusters to the thermodynamics of the hydrated ion and to evolving theoretical approaches that combine high-level calculations on clusters with coarse-grained models of the medium.     

Hydration free energies of monovalent ions in transferable intermolecular potential four point fluctuating charge water: an assessment of simulation methodology and force field performance and transferability

Hydration free energies of nonpolarizable monovalent atomic ions in transferable intermolecular potential four point fluctuating charge (TIP4P-FQ) are computed using several commonly employed ion-water force fields including two complete model sets recently developed for use with the simple water model with four sites and Drude polarizability and TIP4P water models. A simulation methodology is presented which incorporates a number of finite-system free energy corrections within the context of constant pressure molecular dynamics simulations employing the Ewald method and periodic boundary conditions. The agreement of the computed free energies and solvation structures with previously reported results for these models in finite droplet systems indicates good transferability of ion force fields from these water models to TIP4Q-FQ even when ion polarizability is neglected. To assess the performance of the ion models in TIP4P-FQ, we compare with consensus values for single-ion hydration free energies arising from recently improved cluster-pair estimates and a reevaluation of commonly cited, experimentally derived single-ion hydration free energies; we couple the observed consistency of these energies with a justification of the cluster-pair approximation in assigning single-ion hydration free energies to advocate the use of these consensus energies as a benchmark set in the parametrization of future ion force fields.     

Development of new Cd2+ and Pb2+ Lennard-Jones parameters for liquid simulations

We present new Lennard-Jones parameters for Cd2+ and Pb2+ ion-water interactions and describe a general methodology to obtain these parameters for any ion. Our strategy is based on the adjustment of ion parameters to reproduce simultaneously experimental absolute hydration free energy and structural properties, namely, g(r) and coordination numbers, obtained from X-ray liquid scattering and quantum mechanical/molecular mechanical (QM/MM) calculations. The validation of the obtained parameters is made by the calculation of dynamical properties and comparing them with experimental values and theoretical results from the literature. The transferability of parameters is checked by the calculation of thermodynamic, structural, and dynamical properties cited above with four different water models. The results obtained for Cd2+ and Pb2+ show an overall agreement with reference values. The absolute hydration free energy calculated with the TIP3P, SPC/E, SPC, and TIP4P water models presents, respectively, percent differences of 3.8, 3.0, 4.3, and 7.2% for lead(II) and 9.8, 8.4, 10.2, and 14.1% for cadmium(II) when compared with experimental values. Ion-water mean distance and coordination numbers for the first coordination shell are in good agreement with experimental and QM/MM results for both ions. Cd2+ shows a lesser diffusion coefficient compared to that of Pb2+ despite its smaller atomic radius, indicating a more persistent first coordination shell for the cadmium(II) ion, a result confirmed with calculations of the mean residence time of water molecules in the first coordination shell.     

A theoretical study on anomalous temperature dependence of pKw of water

pH, with its well-known value of 7 at ambient condition, is a most basic property of water, with wide implications in chemistry and biology. The pH value is determined by the tendency of autoionization of water molecules into ion pairs, H(+) and OH(-), and is expected to vary extensively with the water condition, which determines the stability of the ion pairs. When temperature rises from the normal to the supercritical region, the pH of water experimentally exhibits complex, nonmonotonic temperature dependence, that is, it first decreases from 7 and then increases rapidly. Accurate theoretical evaluation of pH and microscopic understanding of this anomalous behavior have proven to be a challenging task because the hydration of these ions, especially for OH(-), is very difficult to reproduce. In the present study a molecular simulation is performed to understand this peculiar temperature dependence. The imbalance between the ion-water and the water-water molecular interaction strengths and the concomitant water density enhancement in the hydration shell, observed in the supercritical liquids, serve to put a subtle balance to produce this temperature dependence of the pH value. It is found that the large charge transfers from H(+) and OH(-) to the surrounding water molecules take place. In these transfers, not only water molecules in the neighboring hydration shell but also those in the outer hydration shell play a significant role. The coordination number of water molecules around OH(-) is found to be 4.5 at 300 K, which decreases slowly with temperature, for example, 4 at 800 K, in the present calculation.     

Crystal lattice properties fully determine short-range interaction parameters for alkali and halide ions

Accurate models of alkali and halide ions in aqueous solution are necessary for computer simulations of a broad variety of systems. Previous efforts to develop ion force fields have generally focused on reproducing experimental measurements of aqueous solution properties such as hydration free energies and ion-water distribution functions. This dependency limits transferability of the resulting parameters because of the variety and known limitations of water models. We present a solvent-independent approach to calibrating ion parameters based exclusively on crystal lattice properties. Our procedure relies on minimization of lattice sums to calculate lattice energies and interionic distances instead of equilibrium ensemble simulations of dense fluids. The gain in computational efficiency enables simultaneous optimization of all parameters for Li+, Na+, K+, Rb+, Cs+, F-, Cl-, Br-, and I- subject to constraints that enforce consistency with periodic table trends. We demonstrate the method by presenting lattice-derived parameters for the primitive model and the Lennard-Jones model with Lorentz-Berthelot mixing rules. The resulting parameters successfully reproduce the lattice properties used to derive them and are free from the influence of any water model. To assess the transferability of the Lennard-Jones parameters to aqueous systems, we used them to estimate hydration free energies and found that the results were in quantitative agreement with experimentally measured values. These lattice-derived parameters are applicable in simulations where coupling of ion parameters to a particular solvent model is undesirable. The simplicity and low computational demands of the calibration procedure make it suitable for parametrization of crystallizable ions in a variety of force fields.     

Recent advances in computational actinoid chemistry

We briefly review advances in computational actinoid (An) chemistry during the past ten years in regard to two issues: the geometrical and electronic structures, and reactions. The former addresses the An-O, An-C, and M-An (M is a metal atom including An) bonds in the actinoid molecular systems, including actinoid oxo and oxide species, actinoid-carbenoid, dinuclear and diatomic systems, and the latter the hydration and ligand exchange, the disproportionation, the oxidation, the reduction of uranyl, hydroamination, and the photolysis of uranium azide. Concerning their relevance to the electronic structures and reactions of actinoids and their importance in the development of an advanced nuclear fuel cycle, we also mentioned the work on actinoid carbides and nitrides, which have been proposed to be candidates of the next generation of nuclear fuel, and the oxidation of PuO(x), which is important to understand the speciation of actinoids in the environment, followed by a brief discussion on the urgent need for a heavier involvement of computational actinoid chemistry in developing advanced reprocessing protocols of spent nuclear fuel. The paper is concluded with an outlook.     

Molecular Dynamics Simulation of Mg2+ and Ca2+ Ions in Water

Molecular dynamics simulations of single Mg²⁺ and Ca²⁺ ions in water have been carried out. Different ion-water potentials from the literature have been used, whereas the same water potential, a rigid simple point charged model, has been considered in all the simulations. Structural, thermodynamic, and dynamic properties have been calculated, and the results for different potentials have been compared with available experimental data. The study includes ion–water radial distribution functions, coordination numbers, solution enthalpies, hydration free energies, self-diffusion coefficients, and reorientational times of water molecules in the hydration shells.     

Molecular simulation analysis and X-ray absorption measurement of Ca2+, K+ and Cl- ions in solution

This paper presents recent advances in the use of molecular simulations and extended X-ray absorption fine structure (EXAFS) spectroscopy, which enable us to understand solvated ions in solution. We report and discuss the EXAFS spectra and related properties governing solvation processes of different ions in water and methanol. Molecular dynamics (MD) trajectories are coupled to electron scattering simulations to generate the MD-EXAFS spectra, which are found to be in very good agreement with the corresponding experimental measurements. From these simulated spectra, the ion-oxygen distances for the first hydration shell are in agreement with experiment within 0.05-0.1 A. The ionic species studied range from monovalent to divalent, positive and negative: K+, Ca2+, and Cl-. This work demonstrates that the combination of MD-EXAFS and the corresponding experimental measurement provides a powerful tool in the analysis of the solvation structure of aqueous ionic solutions. We also investigate the value of electronic structure analysis of small aqueous clusters as a benchmark to the empirical potentials. In a novel computational approach, we determine the Debye-Waller factors for Ca2+, K+, and Cl- in water by combining the harmonic analysis of data obtained from electronic structure calculations on finite ion-water clusters, providing excellent agreement with the experimental values, and discuss how they compare with results from a harmonic classical statistical mechanical analysis of an empirical potential.     

Structure and dynamics of the CrIII ion in aqueous solution: Ab initio QM/MM molecular dynamics simulation

Structural and dynamical properties of the Cr(III) ion in aqueous solution have been investigated using a combined ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulation. The hydration structure of Cr(III) was determined in terms of radial distribution functions, coordination numbers, and angular distributions. The QM/MM simulation gives coordination numbers of 6 and 15.4 for the first and second hydration shell, respectively. The first hydration shell is kinetically very inert but by no means rigid and variations of the first hydration shell geometry lead to distinct splitting in the vibrational spectra of Cr(H(2)O)(6) (3+). A mean residence time of 22 ps was obtained for water ligands residing in the second hydration shell, which is remarkably shorter than the experimentally estimated value. The hydration energy of -1108 +/- 7 kcal/mol, obtained from the QM/MM simulation, corresponds well to the experimental hydration enthalpy value.     

Car-Parrinello molecular dynamics simulation of Fe 3+ (aq)

The optimized geometry and energetic properties of Fe(D2O)n 3+ clusters, with n = 4 and 6, have been studied with density-functional theory calculations and the BLYP functional, and the hydration of a single Fe 3+ ion in a periodic box with 32 water molecules at room temperature has been studied with Car-Parrinello molecular dynamics and the same functional. We have compared the results from the CPMD simulation with classical MD simulations, using a flexible SPC-based water model and the same number of water molecules, to evaluate the relative strengths and weaknesses of the two MD methods. The classical MD simulations and the CPMD simulations both give Fe-water distances in good agreement with experiment, but for the intramolecular vibrations, the classical MD yields considerably better absolute frequencies and ion-induced frequency shifts. On the other hand, the CPMD method performs considerably better than the classical MD in describing the intramolecular geometry of the water molecule in the first hydration shell and the average first shell...second shell hydrogen-bond distance. Differences between the two methods are also found with respect to the second-shell water orientations. The effect of the small box size (32 vs 512 water molecules) was evaluated by comparing results from classical simulations using different box sizes; non-negligible effects are found for the ion-water distance and the tilt angles of the water molecules in the second hydration shell and for the O-D stretching vibrational frequencies of the water molecules in the first hydration shell.     

Dynamics of halide ion-water hydrogen bonds in aqueous solutions: dependence on ion size and temperature

We have carried out a series of molecular dynamics simulations to investigate the dynamics of X(-)-water (X = F, Cl, Br, and I) and water-water hydrogen bonds in aqueous alkali halide solutions at room temperature and also of Cl(-)-water and water-water hydrogen bonds at seven different temperatures ranging from 238 to 318 K. The hydrogen bonds are defined by using a set of configurational criteria with respect to the anion(oxygen)-oxygen and anion(oxygen)-hydrogen distances and the anion(oxygen)-oxygen-hydrogen angle for an anion(water)-water pair. The results of the hydrogen bond dynamics are obtained for two different cutoff values for the angular criterion. In both cases, similar dynamical behavior of the hydrogen bonds is found with respect to their dependence on ion size and temperature. The fluoride ion-water hydrogen bonds are found to break at a much slower rate than water-water hydrogen bonds, while the lifetimes of chloride and bromide ion-water hydrogen bonds are found to be shorter than those of fluoride ion-water ones but still longer than water-water hydrogen bonds. The short-time dynamics of iodide ion-water hydrogen bonds is found to be slightly faster, while its long-time dynamics is found to be slightly slower than the corresponding water-water hydrogen bond dynamics. Correlations of the observed dynamics of anion(water)-water hydrogen bonds with those of rotational and translational diffusion and residence times of water molecules in ion(water) hydration shells are also discussed. With variation of temperature, the lifetimes of both Cl(-)-water and water-water hydrogen bonds are found to show Arrhenius behavior with a slightly higher activation energy for the Cl(-)-water hydrogen bonds.     

Structural variations across the lanthanide series of macrocyclic DOTA complexes: insights into the design of contrast agents for magnetic resonance imaging

It was early shown that the macrocyclic Ln(DOTA) complexes (DOTA = 1,4,7,10-tetra-azacyclododecane-N,N',N' ',N' "-tetraacetic acid) exists in solution as a mixture of two enantiomeric pairs of diastereoisomers differing in the ligand conformation, namely, square antiprismatic (SA) and twisted square antiprismatic (TSA) geometries, respectively. Later, extensive (1)H NMR investigations suggested that a coordination change may be superimposed on this conformational equilibrium involving two additional structures in which the metal ion possesses a coordination number of eight (CN 8). It was predicted that these two species, lacking the apical coordinated water molecule, would maintain the SA and TSA coordination geometries, and therefore, they have been labeled as SA' and TSA', respectively. In this work we report the X-ray solid-state crystal structure determination of six Ln(DOTA) complexes representative of all four coordination geometry typologies deduced from NMR solution studies. A distinctive structural feature that discriminates SA (and SA') and TSA (and TSA') structures is represented by the twist angle between the two square planes of the antiprism, the basal four nitrogen, and the apical four oxygen planes. [Ce(DOTA)(H(2)O)](-) displays a TSA structural typology with a twist angle of 25 degrees and a Ce-O(water) distance of 2.59 A. The SA-type structure has been found in the case of complexes with Pr(III), Nd(III), and Dy(III), where the twist angle is 39, 39, and 38 degrees, respectively, and the metal-water oxygen distance varies significantly (Pr-O(w) 2.529 A; Nd-O(w) 2.508 A; and Dy-O(w) 2.474 A). [Tm(DOTA)](-) displays a TSA'-type structure with a twist angle of 24 degrees. As compared with the TSA structure of the corresponding Ce(III) complex, the Tm(III) complex shows an overall marked shrinkage of all metal-nitrogen and metal-oxygen distances (ca. 0.2 A), which reflects the contraction of the metal ionic radius across the series but also the effect associated with the decrease of the CN from 9 to 8. In [Sc(DOTA)](-), the even smaller ionic radius of Sc(III) shifts the geometry of the coordination cage to the more compact SA' typology with a twist angle of 41 degrees, a value very similar to that found in the SA structures of lanthanide(III) ions with CN 9. Finally, an investigation was made into the hydration spheres of the complexes with SA and TSA geometries to account for the experimental evidence of a markedly different rate of water exchange for the two isomeric structures. This is of fundamental importance to the understanding of the corresponding Gd(III) complexes as MRI contrast agents.     

Speciation of the curium(III) ion in aqueous solution: a combined study by quantum chemistry and molecular dynamics simulation

The structures of aquo complexes of the curium(III) ion have been systematically studied using quantum chemical and molecular dynamics (MD) methods. The first hydration shell of the Cm3+ ion has been calculated using density functional theory (DFT), with and without inclusion of the conductor-like polarizable continuum medium (CPCM) model of solvation. The calculated results indicate that the primary hydration number of Cm3+ is nine, with a Cm-O bond distance of 2.47-2.48 A. The calculated bond distances and the hydration number are in excellent agreement with available experimental data. The inclusion of a complete second hydration shell of Cm3+ has been investigated using both DFT and MD methods. The presence of the second hydration shell has significant effects on the primary coordination sphere, suggesting that the explicit inclusion of second-shell effects is important for understanding the nature of the first shell. The calculated results indicate that 21 water molecules can be coordinated in the second hydration shell of the Cm3+ ion. MD simulations within the hydrated-ion model suggest that the second-shell water molecules exchange with the bulk solvent with a lifetime of 161 ps.     

Study of the structure of molecular complexes

A cluster of 200 molecules of water containing one of the LiF, LiCl, NaF, NaCl, KF or KCl ion pairs has been studied at the temperature T= 298°K using Monte Carlo techniques. The anion-cation internuclear separations considered in this work for any of the above pairs are 6.0 Å, 8.0 Å and 10.0 Å. The water-water potential is obtained from quantum-mechanical Hartree-Fock type computations corrected by inclusion of dispersion forces; the ion-water potentials have been obtained from Hartree-Fock type computations on the single ion-water complex. The computed radii for the first hydration shell are 2.7±0.1 Å, 3.4±0.3 Å, 4.0±0.3 Å, 3.0±0.5 Å, and 3.9±0.4 Å, for Li⁺, Na⁺, K⁺, F^– and Cl^–, respectively. The computed coordination numbers are 5.4±0.7,6.0±1.1, 7.2±1.2,4.5±0.6 and 5.1±0.8 for the same ions, respectively. The range of the coordination number obtained from compressibility, enthalpy, NMR spectroscopy and other experimental methods is much larger than the error ranges above given. Therefore the Monte Carlo simulation provides reliable information on the cluster shape, cluster structure and on the coordination numbers and hydration shell radii for the cations and anions, when both are present in a water cluster.     

Vibrational spectroscopy of water in hydrated lipid multi-bilayers. I. Infrared spectra and ultrafast pump-probe observables

The vibrational spectroscopy of hydration water in dilauroylphosphatidylcholine lipid multi-bilayers is investigated using molecular dynamics simulations and a mixed quantum/classical model for the OD stretch spectroscopy of dilute HDO in H(2)O. FTIR absorption spectra, and isotropic and anisotropic pump-probe decay curves have been measured experimentally as a function of the hydration level of the lipid multi-bilayer, and our goal is to make connection with these experiments. To this end, we use third-order response functions, which allow us to include non-Gaussian frequency fluctuations, non-Condon effects, molecular rotations, and a fluctuating vibrational lifetime, all of which we believe are important for this system. We calculate the response functions using existing transition frequency and dipole maps. From the experiments it appears that there are two distinct vibrational lifetimes corresponding to HDO molecules in different molecular environments. In order to obtain these lifetimes, we consider a simple two-population model for hydration water hydrogen bonds. Assuming a different lifetime for each population, we then calculate the isotropic pump-probe decay, fitting to experiment to obtain the two lifetimes for each hydration level. With these lifetimes in hand, we then calculate FTIR spectra and pump-probe anisotropy decay as a function of hydration. This approach, therefore, permits a consistent calculation of all observables within a unified computational scheme. Our theoretical results are all in qualitative agreement with experiment. The vibrational lifetime of lipid-associated OD groups is found to be systematically shorter than that of the water-associated population, and the lifetimes of each population increase with decreasing hydration, in agreement with previous analysis. Our theoretical FTIR absorption spectra successfully reproduce the experimentally observed red-shift with decreasing lipid hydration, and we confirm a previous interpretation that this shift results from the hydrogen bonding of water to the lipid phosphate group. From the pump-probe anisotropy decay, we confirm that the reorientational motions of water molecules slow significantly as hydration decreases, with water bound in the lipid carbonyl region undergoing the slowest rotations.     

Steric effects control the structure of the solvated lanthanum(III) ion in aqueous, dimethyl sulfoxide, and N,N'-dimethylpropyleneurea solution. An EXAFS and large-angle X-ray scattering study

The structure of the solvated lanthanum(III) ion has been determined in aqueous, dimethyl sulfoxide, and N,N'-dimethylpropyleneurea solution by means of the EXAFS and large-angle X-ray scattering (LAXS) techniques. The close agreement between the EXAFS spectra of solid nonaaqualanthanum(III) trifluoromethanesulfonate and of an aqueous lanthanum(III) perchlorate solution shows that the hydrated lanthanum(III) ion in aqueous solution most probably has the same structure as in the solid, i.e., nine water molecules coordinated in a tricapped trigonal prismatic configuration. The data analysis from EXAFS and LAXS measurements of the aqueous solution resulted in the La-O bond distances 2.52(2) and 2.65(3) A to the water molecules in the prism and the capping positions, respectively. The LAXS study shows a second hydration sphere consistent with approximately 18 water molecules at 4.63(2) A. The EXAFS spectra of solid octakis(dimethyl sulfoxide)lanthanum(III) trifluoromethanesulfonate and a dimethyl sulfoxide solution of this salt are also similar. The data analysis of EXAFS and LAXS measurements assuming eight-coordination around lanthanum yielded an La-O bond distance of 2.50(2) A, and an La...S distance of 3.70(3) A, giving an La-O-S angle of 133(2) degrees. The EXAFS data of an N,N'-dimethylpropyleneurea solution of lanthanum(III) trifluoromethanesulfonate gave the La-O bond distance 2.438(4) A and the La...C distance 3.41(2) A, which correspond to an La-O-C angle of 131(2) degrees. The La-O bond distance is consistent with seven-coordination around lanthanum, on the basis of the variation of the ionic radii of the lanthanum(III) ion with different coordination numbers.