Incorporating solvent effects in DFT: insights from cation exchange in faujasites

Zeolites are versatile materials renowned for their extra-framework cation exchange capabilities, with applications spanning diverse fields, including nuclear waste treatment. While detailed experimental characterization offers valuable insight, density functional theory (DFT) proves particularly adept at investigating ion exchange in zeolites, owing to its atomic and electronic resolution. However, the prevalent occurrence of zeolitic ion exchange in aqueous environments poses a challenge to conventional DFT modeling, traditionally conducted in a vacuum. This study seeks to enhance zeolite modeling by systematically evaluating predictive differences across varying degrees of aqueous solvent inclusion. Specifically focusing on monovalent cation exchange in Na-X zeolites, we explore diverse modeling approaches. These range from simple dehydrated systems (representing bare reference states in vacuum) to more sophisticated models that incorporate aqueous solvent effects through explicit water molecules and/or a dielectric medium. Through comparative analysis of DFT and semi-empirical DFT approaches, along with their validation against experimental results, our findings underscore the necessity to concurrently consider explicit and implicit solvent effects for accurate prediction of zeolitic ionic exchange.

Ion Solvation Free Energy Calculation Based on Ab Initio Molecular Dynamics Using a Hybrid Solvent Model

Free energy calculation of small molecules or ion species in aqueous solvent is one of the most important problems in electrochemistry study. Although there are many previous approaches to calculate such free energies, they are based on ab initio methods and suffer from various limitations and approximations. In the current work, we developed a hybrid approach based on ab initio molecular dynamics (AIMD) simulations to calculate the ion solvation energy. In this approach, a small water cluster surrounding the central ion is used, and implicit solvent model is applied outside the water cluster. A dynamic potential well is used during AIMD to keep the water cluster together. Quasi-harmonic approximation is used to calculate the entropy contribution, while the total energy average is used to calculate the enthalpy term. The obtained solvation voltages of the bulk metal agree with experiments within 0.3 eV, and the simulation results for the solvation energies of gaseous ions are close to the experimental observations. Besides the free energies, radial pair distribution functions and coordination numbers of hydrated cations are also obtained. The remaining challenges of this method are also discussed.

Ion-ion interactions enhance aluminum solubility in alkaline suspensions of nano-gibbsite (α-Al(OH)3) with sodium nitrite/nitrate

Despite widespread industrial importance, predicting metal solubilities in highly concentrated, multicomponent aqueous solutions is difficult due to poorly understood ion-ion and ion-solvent interactions. Aluminum hydroxide solid phase solubility in concentrated sodium hydroxide (NaOH) solutions is one such case, with major implications for ore refining, as well as processing of radioactive waste stored at U.S. Department of Energy legacy sites, such as the Hanford Site, Washington State. The solubility of gibbsite (α-Al(OH)₃) is often not well predicted because other ions affect the activity of hydroxide (OH^-) and aluminate (Al(OH)₄^-) anions. In the present study, we systematically examined the influence of key anions, nitrite (NO₂^-) and nitrate (NO₃^-), as sodium salts on the solubility of α-Al(OH)₃ in NaOH solutions taking care to establish equilibrium from both under- and oversaturation. Rapid equilibration was enabled by use of a highly pure and crystalline synthetic nano-gibbsite of well-defined particle size and shape. Measured dissolved aluminum concentrations were compared with those predicted by an α-Al(OH)₃ solubility model derived for simple Al(OH)₄^-/OH^- systems. Specific anion effects were expressed as an enhancement factor (Al_enhc) conveying the excess of dissolved aluminum. At 45 °C, NaNO₂ and NaNO₃-containing systems exhibited Al_enhc values of 2.70 and 1.88, respectively, indicating significant enhancement. The solutions were examined by Raman and high-field ²⁷Al NMR spectroscopy, indicating specific interactions including Al(OH)₄^--Na⁺ contact ion pairing and Al(OH)₄^--NO₂^-/NO₃^- ion-ion interactions. Dynamic evolution of the α-Al(OH)₃ particles including growth and agglomeration was observed revealing the importance of dissolution/reprecipitation in establishing equilibrium. These studies indicate that incomplete ion hydration, as a result of the low water activity in these concentrated electrolytes, results in: (i) enhanced reactivity of the hydroxide ion with respect to α-Al(OH)₃; (ii) increased concentrations of Al(OH)₄^- in solution; and (iii) stronger ion-ion interactions that act to stabilize the supersaturated solutions. This information on the mechanisms by which α-Al(OH)₃ becomes supersaturated is essential for more energy-efficient aluminum processing technologies, including the treatment of millions of gallons of Al(OH)₄^--rich high-level radioactive waste.

Multinuclear Magnetic Resonance Study of Sodium Salts in Water Solutions

The small amounts of gaseous 3He dissolved in low concentrated water solutions of NaCl, NaNO3 and NaClO4 were prepared and examined by 3He-, 23Na-, 35Cl- and 15N-NMR spectroscopy. This experimental data, along with new theoretical shielding factors, was used to measure the 23Na nuclear magnetic moment against that of helium-3 μ(23Na) = +2.2174997(111) in nuclear magnetons. The standard relationship between NMR frequencies and nuclear magnetic moments of observed nuclei was used. The nuclear magnetic shielding factors of 23Na cation were verified against that of counter ions present in water solutions. Very good agreement between shielding constants σ(3He), σ(23Na+), σ(35Cl‒), σ(35ClO4‒), σ(15NO3‒) in water at infinite dilution and nuclear magnetic moments was observed for all magnetic nuclei. It can be used as a reference nucleus for calculating a few other magnetic moments of different nuclei by the NMR method. An analysis of new and former μ(23Na) experimental data obtained by the atomic beam magnetic resonance method (ABMR) and other NMR measurements shows good replicability of all specified results. The composition of sodium water complexes was discussed in terms of chemical equilibria and NMR shielding scale.

Importance of van der Waals effects on the hydration of metal ions from the Hofmeister series

The van der Waals (vdW) interaction plays a crucial role in the description of liquid water. Based on ab initio molecular dynamics simulations, including the non-local and fully self-consistent density-dependent implementation of the Tkatchenko-Scheffler dispersion correction, we systematically studied the aqueous solutions of metal ions (K⁺, Na⁺, and Ca²⁺) from the Hofmeister series. Similar to liquid water, the vdW interactions strengthen the attractions among water molecules in the long-range, leading to the hydrogen bond networks softened in all the ion solutions. However, the degree that the hydration structure is revised by the vdW interactions is distinct for different ions, depending on the strength of short-range interactions between the hydrated ion and surrounding water molecules. Such revisions by the vdW interactions are important for the understanding of biological functionalities of ion channels.

Salt Solubilities in Aqueous Solutions of NaNO3, NaNO2, NaCl, and NaOH: A Hofmeister-like Series for Understanding Alkaline Nuclear Waste

Nonelectrolyte solubility in electrolyte solutions follow the Hofmeister series, but the applicability of the series to salt solubility has been less appreciated. This study, using solubility data for thirteen sodium-bearing salts, shows that salts are consistently salted out by electrolytes important to alkaline nuclear waste in the order NaOH > NaCl > NaNO₂ > NaNO₃ at 298.15 K, which is the same order as the Hofmeister series. Graphical presentation allowed for easy separation of the common ion effect (caused by the addition of Na⁺) from the salting-out effect (caused by the presence of anions) because there is a large difference between the solubility of a given salt in different background electrolytes at a common Na⁺ molality. The trend persists even in very high electrolyte concentrations where essentially all of the water molecules must be in the coordination sphere of an ion, which means that the effect of electrolytes on "bulk water" is not the cause of the trend. These specific interactions more likely result from the sharing of water molecules between ions, augmented by differences in ion-pairing of the electrolytes. The Hofmeister series has practical application to the management of alkaline high-level radioactive waste created at nuclear fuel reprocessing facilities, where a predictive understanding of salt solubility is essential for blending wastes of disparate compositions prior to treatment.

A study of the hydration of the alkali metal ions in aqueous solution

The hydration of the alkali metal ions in aqueous solution has been studied by large angle X-ray scattering (LAXS) and double difference infrared spectroscopy (DDIR). The structures of the dimethyl sulfoxide solvated alkali metal ions in solution have been determined to support the studies in aqueous solution. The results of the LAXS and DDIR measurements show that the sodium, potassium, rubidium and cesium ions all are weakly hydrated with only a single shell of water molecules. The smaller lithium ion is more strongly hydrated, most probably with a second hydration shell present. The influence of the rubidium and cesium ions on the water structure was found to be very weak, and it was not possible to quantify this effect in a reliable way due to insufficient separation of the O–D stretching bands of partially deuterated water bound to these metal ions and the O–D stretching bands of the bulk water. Aqueous solutions of sodium, potassium and cesium iodide and cesium and lithium hydroxide have been studied by LAXS and M–O bond distances have been determined fairly accurately except for lithium. However, the number of water molecules binding to the alkali metal ions is very difficult to determine from the LAXS measurements as the number of distances and the temperature factor are strongly correlated. A thorough analysis of M–O bond distances in solid alkali metal compounds with ligands binding through oxygen has been made from available structure databases. There is relatively strong correlation between M–O bond distances and coordination numbers also for the alkali metal ions even though the M–O interactions are weak and the number of complexes of potassium, rubidium and cesium with well-defined coordination geometry is very small. The mean M–O bond distance in the hydrated sodium, potassium, rubidium and cesium ions in aqueous solution have been determined to be 2.43(2), 2.81(1), 2.98(1) and 3.07(1) Å, which corresponds to six-, seven-, eight- and eight-coordination. These coordination numbers are supported by the linear relationship of the hydration enthalpies and the M–O bond distances. This correlation indicates that the hydrated lithium ion is four-coordinate in aqueous solution. New ionic radii are proposed for four- and six-coordinate lithium(I), 0.60 and 0.79 Å, respectively, as well as for five- and six-coordinate sodium(I), 1.02 and 1.07 Å, respectively. The ionic radii for six- and seven-coordinate K⁺, 1.38 and 1.46 Å, respectively, and eight-coordinate Rb⁺ and Cs⁺, 1.64 and 1.73 Å, respectively, are confirmed from previous studies. The M–O bond distances in dimethyl sulfoxide solvated sodium, potassium, rubidium and cesium ions in solution are very similar to those observed in aqueous solution.

The hydration of alkali metal ions has been studied by large angle X-ray scattering, LAXS, and double difference infrared spectroscopy. The obtained M−O bond distances from LAXS have been compared to relevant crystal structures, conclusions about hydration numbers in aqueous solution have been made, and new ionic radii have been proposed. Hydration numbers of six, seven, eight and eight are proposed for the sodium, potassium, rubidium and cesium ions in aqueous solution.

ForceFit: a code to fit classical force fields to quantum mechanical potential energy surfaces

The ForceFit program package has been developed for fitting classical force field parameters based upon a force matching algorithm to quantum mechanical gradients of configurations that span the potential energy surface of the system. The program, which runs under UNIX and is written in C++, is an easy-to-use, nonproprietary platform that enables gradient fitting of a wide variety of functional force field forms to quantum mechanical information obtained from an array of common electronic structure codes. All aspects of the fitting process are run from a graphical user interface, from the parsing of quantum mechanical data, assembling of a potential energy surface database, setting the force field, and variables to be optimized, choosing a molecular mechanics code for comparison to the reference data, and finally, the initiation of a least squares minimization algorithm. Furthermore, the code is based on a modular templated code design that enables the facile addition of new functionality to the program.