Neutron Scattering Studies of the Hydration Structure of Li+

Anionic Effects on Concentrated Aqueous Lithium Ion Dynamics

The dynamics, orientational anisotropy, diffusivity, viscosity, and density were measured for concentrated lithium salt solutions, including lithium chloride (LiCl), lithium bromide (LiBr), lithium nitrite (LiNO2), and lithium nitrate (LiNO3), with methyl thiocyanate as an infrared vibrational probe molecule, using two-dimensional infrared spectroscopy (2D IR), nuclear magnetic resonance (NMR) spectroscopy, and viscometry. The 2D IR, NMR, and viscosity results show that LiNO2 exhibits longer correlation times, lower diffusivity, and nearly 4 times greater viscosity compared to those of the other lithium salt solutions of the same concentration, suggesting that nitrite anions may strongly facilitate structure formation via strengthening water-ion network interactions, directly impacting bulk solution properties at sufficiently high concentrations. Additionally, the LiNO2 and LiNO3 solutions show significantly weakened chemical interactions between the lithium cations and the methyl thiocyanate when compared with those of the lithium halide salts.

Characterization of the Coordination and Solvation Dynamics of Solvated Systems─Implications for the Analysis of Molecular Interactions in Solutions and Pure H2O

The characterization of solvation shells of atoms, ions, and molecules in solution is essential to relate solvation properties to chemical phenomena such as complex formation and reactivity. Different definitions of the first-shell coordination sphere from simulation data can lead to potentially conflicting data on the structural properties and associated ligand exchange dynamics. The definition of a solvation shell is typically based on a given threshold distance determined from the respective solute-solvent pair distribution function g(r) (i.e., GC). Alternatively, a nearest neighbor (NN) assignment based on geometric properties of the coordination complex without the need for a predetermined cutoff criterion, such as the relative angular distance (RAD) or the modified Voronoi (MV) tessellation, can be applied. In this study, the effect of different NN algorithms on the coordination number and ligand exchange dynamics evaluated for a series of monatomic ions in aqueous solution, carbon dioxide in aqueous and dichloromethane solutions, and pure liquid water has been investigated. In the case of the monatomic ions, the RAD approach is superior in achieving a well separated definition of the first solvation layer. In contrast, the MV algorithm provides a better separation of the NNs from a molecular point of view, leading to better results in the case of solvated CO2. When analyzing the coordination environment in pure water, the cutoff-based GC framework was found to be the most reliable approach. By comparison of the number of ligand exchange reactions and the associated mean ligand residence times (MRTs) with the properties of the coordination number autocorrelation functions, it is shown that although the average coordination numbers are sensitive to the different definitions of the first solvation shell, highly consistent estimates for the associated MRT of the solvated system are obtained in the majority of cases.

Structure and dynamics of the Li+ ion in water, methanol and acetonitrile solvents: ab initio molecular dynamics simulations

Fundamental understanding of the structure and dynamics of the Li+ ion in solution is of utmost importance in different fields of science and technology, especially in the field of ion batteries. In view of this, ab initio molecular dynamics (AIMD) simulations of the LiCl salt in water, methanol and acetonitrile were performed to elucidate structural parameters such as radial distribution function and coordination number, and dynamical properties like diffusion coefficient, limiting ion conductivity and hydrogen bond correlation function. In the present AIMD simulation, one LiCl in water is equivalent to 0.8 M, which is close to the concentration of the lithium salt used in the Li-ion battery. The first sphere of coordination number of the Li+ ion was reaffirmed to be 4. The radial distribution function for different pairs of atoms is seen to be in good agreement with the experimental results. The calculated potential of mean force indicates the stronger interaction of the Li+ ion with methanol over water followed by acetonitrile. The dynamical parameters convey quite high diffusion and limiting ionic conductivity of the Li+ ion in acetonitrile compared to that in water and methanol which has been attributed to the transport of the Li-Cl ion pair in a non-dissociated form in acetonitrile. The AIMD results were found to be in accordance with the experimental findings, i.e. the limiting ion conductivity was found to follow the order acetonitrile > methanol > water. This study shows the importance of atomistic level simulations in evaluating the structural and dynamical parameters and in implementing the results for predicting and synthesizing better next generation solvents for lithium ion batteries (LIBs).

Binding of carboxylate and water to monovalent cations

The interactions of carboxylate anions with water and cations are important for a wide variety of systems, both biological and synthetic. To gain insight on properties of the local complexes, we apply density functional theory, to treat the complex electrostatic interactions, and investigate mixtures with varied numbers of carboxylate anions (acetate) and waters binding to monovalent cations, Li+, Na+ and K+. The optimal structure with overall lowest free energy contains two acetates and two waters such that the cation is four-fold coordinated, similar to structures found earlier for pure water or pure carboxylate ligands. More generally, the complexes with two acetates have the lowest free energy. In transitioning from the overall optimal state, exchanging an acetate for water has a lower free energy barrier than exchanging water for an acetate. In most cases, the carboxylates are monodentate and in the first solvation shell. As water is added to the system, hydrogen bonding between waters and carboxylate O atoms further stabilizes monodentate structures. These structures, which have strong electrostatic interactions that involve hydrogen bonds of varying strength, are significantly polarized, with ChelpG partial charges that vary substantially as the bonding geometry varies. Overall, these results emphasize the increasing importance of water as a component of binding sites as the number of ligands increases, thus affecting the preferential solvation of specific metal ions and clarifying Hofmeister effects. Finally, structural analysis correlated with free energy analysis supports the idea that binding to more than the preferred number of carboxylates under architectural constraints are a key to ion transport.

Ab Initio Molecular Dynamics Investigation of the Solvation States of Hydrated Ions in Confined Water

Ionic transport in nanoscale channels with a critical size comparable to that of ions and solutes exhibits exceptional performance in water desalination, ion separation, electrocatalysts, and supercapacitors. However, the solvation states (SSs), i.e., the hydration structures and probability distribution, of hydrated ions in nanochannels differ from those in the bulk and the perspective of continuum theory. In this work, we conduct ab initio enhanced-sampling atomistic simulations to investigate the ion-specific SSs of monovalent ions (including Li+, Na+, K+, F-, Cl-, and I-) in the graphene channel with a width of 1 nm. Our findings highlight that the SSs of those ions are primarily determined by ion-water hydration, where ion-wall interactions play a minor role. The distribution of ions in layered confined water is a result of ion-specific hydration, which arises from the synergy of entropy and enthalpy. The free energy barriers for transitions between SSs are on the order of 1kBT, allowing for modulation through applying external fields or modifying surface properties. As the ion-wall interaction strengthens, as observed in vermiculite and carbides and nitrides of transition metal channels, the probability of near-wall SSs increases. These results help to improve the performance of nanofluidic devices and provide crucial insights for developing accurate force fields of molecular simulations or advanced theoretical approaches for ion dynamics in confined channels.

Real-time visualisation of ion exchange in molecularly confined spaces where electric double layers overlap

Ion interactions with interfaces and transport in confined spaces, where electric double layers overlap, are essential in many areas, ranging from crevice corrosion to understanding and creating nano-fluidic devices at the sub 10 nm scale. Tracking the spatial and temporal evolution of ion exchange, as well as local surface potentials, in such extreme confinement situations is both experimentally and theoretically challenging. Here, we track in real-time the transport processes of ionic species (LiClO4) confined between a negatively charged mica surface and an electrochemically modulated gold surface using a high-speed in situ sensing Surface Forces Apparatus. With millisecond temporal and sub-micrometer spatial resolution we capture the force and distance equilibration of ions in the confinement of D ≈ 2-3 nm in an overlapping electric double layer (EDL) during ion exchange. Our data indicate that an equilibrated ion concentration front progresses with a velocity of 100-200 μm s-1 into a confined nano-slit. This is in the same order of magnitude and in agreement with continuum estimates from diffusive mass transport calculations. We also compare the ion structuring using high resolution imaging, molecular dynamics simulations, and calculations based on a continuum model for the EDL. With this data we can predict the amount of ion exchange, as well as the force between the two surfaces due to overlapping EDLs, and critically discuss experimental and theoretical limitations and possibilities.

Hydration of Alkali Metal and Halide Ions from Static and Dynamic Viewpoints

Ion hydration in aqueous solutions plays a paramount role in many fields. Despite many studies on ion hydration, the nature of ion hydration is not consistently understood at the molecular level. Combining neutron scattering (NS), wide-angle X-ray scattering (WAXS), and molecular dynamics (MD), we quantify the ionic hydration degree (hydration ability) systematically for a series of alkali metal and halide ions based on static and dynamic hydration numbers. The former is based on the orientational correlation of water molecules bound to an ion derived from the positional information from NS and WAXS. The latter is defined as the mean number of water molecules remaining in the first coordination shell of an ion over a residence time of bound water molecules around the ion from MD. The static and dynamic hydration numbers distinguish hydration from coordination and quantify the ionic hydration degree, which provides a valuable reference for understanding various phenomena in nature.

Phase Diagram of Aqueous Solutions of LiCl: a Study of Concentration Effects on the Anomalies of Water

We perform molecular dynamics simulations in order to study thermodynamics and the structure of supercooled aqueous solutions of lithium chloride (LiCl) at concentrations c = 0.678 and 2.034 mol/kg. We model the solvent using the TIP4P/2005 potential and the ions using the Madrid-2019 force field, a force field particularly suited for studying this solution. We find that, for c = 0.678 mol/kg, the behavior of the equation of state, studied in the P-T plane, indicates the presence of a liquid-liquid phase transition, similar to what was previously found for bulk water. We estimate the position of the liquid-liquid critical point to be at T_c ≈ 174 K, P_c ≈ 1775 bar, and ρ_c ≈ 1.065 g/cm³. When the concentration is tripled to c = 2.034 mol/kg, no critical point is observed, indicating its possible disappearance at this concentration. We also study the water-water and water-ions structure in the two solutions, and we find that at the concentrations examined the effect of ions on the water-water structure is not strong, and all the features found in bulk water are preserved. We also calculate the hydration number of the Li and Cl ions, and in line with experiments, we find the value of 4 for Li⁺ and between 5.5 and 6 for Cl^-, confirming the good performances of the Madrid-2019 force field.

Quantifying the Structure of Water and Hydrated Monovalent Ions by Density Functional Theory-Based Molecular Dynamics

The accurate description of the structures of water and hydrated ions is important in electrochemical desalination, ion separation, and supercapacitors. In this work, we present an ab initio atomistic simulation-based study to explore the structure of water and hydrated monovalent ions (Li⁺, Na⁺, K⁺, Rb⁺, F^-, and Cl^-) at ambient conditions using generalized gradient approximation (GGA)-based methods with and without van der Waals correction (PBE, PBE + D3, and revPBE + D3) and recently developed strongly constrained and appropriately normed (SCAN) meta-GGA. We find that both revPBE + D3 and SCAN can well capture the structure of bulk water with +30 K artificial high temperature in contrast to overstructuring water using PBE and PBE + D3. However, being the same as PBE + D3, revPBE + D3 overestimates the structure of the hydration shell, especially for monovalent cations. Surprisingly, SCAN can well match the experimental results of hydrated monovalent ions. Detailed structure analyzes of entropy reveal that the hydration shell under the level of PBE + D3 and revPBE + D3 is more disordered and looser than SCAN. The successful prediction of the flexible SCAN functional could facilitate the exploration of complex ionic processes in the aqueous phase, the interactions of hydrated ions with surfaces, and solvation states in nanopores at an accurate, efficient, predictive, and ab initio level.

A fundamental study on selective extraction of Li+ with dibenzo-14-crown-4 ether: Toward new technology development for lithium recovery from brines

The present study has proposed a selective Li⁺ extraction process using a novel extractant of dibenzo-14-crown-4 ether functionalized with an alkyl C16 chain (DB14C4-C16) synthesized based on the ion imprinting technology (IIT). Theoretical analysis of the possible complexes formed by DB14C4-C16 with Li⁺ and the competing ions of Na⁺, K⁺, Ca²⁺ and Mg²⁺ was performed through density functional theory (DFT) modeling. The Gibbs free energy change of the complexes of metal ions with DB14C4-C16 and water molecules were calculated to be -125.81 and -166.01 kJ/mol for lithium, -55.73 and -117.77 kJ/mol for sodium, and -196.02 and -291.52 kJ/mol for magnesium, respectively. Furthermore, the solvent extraction experiments were carried out in both single Li⁺ and multi-ions containing solutions, and the results delivered a good selectivity of DB14C4-C16 towards Li⁺ over the competing ions, showing separation coefficients of 68.09 for Ca²⁺-Li⁺, 24.53 for K⁺-Li⁺, 16.32 for Na⁺-Li⁺, and 3.99 for Mg²⁺-Li⁺ under the optimal conditions. The experimental results are generally in agreement with the theoretical calculations.

Role of Counterions in the Adsorption and Micellization Behavior of 1:1 Ionic Surfactants at Fluid Interfaces─Demonstrated by the Standard Amphiphile System of Alkali Perfluoro-n-octanoates

In our latest communication, we proved experimentally that the ionic surfactant's surface excess is exclusively determined by the size of the hydrated counterion.[Lunkenheimer , Langmuir, 2017, 33, 10216-1022410.1021/acs.langmuir.7b00786]. However, at this stage of research, we were unable to decide whether this does only hold for the two or three lightest ions of lithium, sodium, and potassium, respectively. Alternatively, we could also consider the surface excess of the heavier hydrated alkali ions of potassium, rubidium, and cesium, having practically identical ion size, as being determined by the cross-sectional area of the related anionic extended chain residue. The latter assumption has represented state of art. Searching for reliable experimental results on the effect of the heavier counterions on the boundary layer, we have extended investigations to the amphiphiles' solutions of concentrations above the critical concentration of micelle formation (cmc).We provided evidence that the super-micellar solutions' equilibrium surface tension will remain constant provided the required conditions are followed. The related σ_cmc-value represents a parameter characteristic of the ionic surfactant's adsorption and micellization behavior. Evaluating the amphiphile's surface excess obtained from adsorption as a function of the related amphiphile's σ_cmc-value enables you to calculate the radius of the hydrated counterion valid in sub- and super-micellar solution likewise. The σ_cmc-value is directly proportional to the counterion's diameter concerned. Taking additionally into account the radii of naked ions known from crystal research, we succeeded in exactly discriminating the hydrated alkali ions' size from each other. There is a distinct sequence of hydration radii in absolute scale following the inequality, Li⁺ > Na⁺ > K⁺ > (NH₄)⁺ > Rb⁺ > Cs⁺. Therefore, we have to extend our model of counterion effectiveness put forward in our previous communication. It represents a general principle of the counterion effect.

Thermodynamics of Hydration from the Perspective of the Molecular Quasichemical Theory of Solutions

The quasichemical organization of the potential distribution theorem, molecular quasichemical theory (QCT), enables practical calculations and also provides a conceptual framework for molecular hydration phenomena. QCT can be viewed from multiple perspectives: (a) as a way to regularize an ill-conditioned statistical thermodynamic problem; (b) as an introduction of and emphasis on the neighborship characteristics of a solute of interest; or (c) as a way to include accurate electronic structure descriptions of near-neighbor interactions in defensible statistical thermodynamics by clearly defining neighborship clusters. The theory has been applied to solutes of a wide range of chemical complexity, ranging from ions that interact with water with both long-ranged and chemically intricate short-ranged interactions, to solutes that interact with water solely through traditional van der Waals interations, and including water itself. The solutes range in variety from monatomic ions to chemically heterogeneous macromolecules. A notable feature of QCT is that, in applying the theory to this range of solutes, the theory itself provides guidance on the necessary approximations and simplifications that can facilitate the calculations. In this Perspective, we develop these ideas and document them with examples that reveal the insights that can be extracted using the QCT formulation.

Resolving the Equal Number Density Puzzle: Molecular Picture from Simulations of LiCl(aq) and NaCl(aq)

The change in number densities of aqueous solutions of alkali chlorides should be qualitatively predictable. Typically, as cations get larger, the number density of the solution decreases. However, aqueous solutions of lithium and sodium chloride exhibit at ambient conditions practically identical number densities at equal molalities despite different ionic sizes. Here, we provide an atomistic interpretation of this experimentally observed anomalous behavior using molecular dynamics simulations. The obtained results show that the rigidity of the Li⁺ first and second solvation shells and the associated compromised hydrogen bonding result in practically equal average water densities in the local hydration regions for Li⁺ and Na⁺ despite different sizes of the cations. In addition, in more distant regions from the cations, the water densities of these two solutions also coincide. These findings thus provide an atomistic interpretation for matching number densities of LiCl and NaCl solutions. In contrast, the number density differences between NaCl and KCl solutions as well as between LiCl and KCl solutions behave in a regular fashion with lower number densities of solutions observed for larger cations.

Surface Forces and Structure in a Water-in-Salt Electrolyte

Water-in-salt electrolytes are a fascinating new class of highly concentrated aqueous solutions with wide electrochemical stability windows that make them viable as aqueous battery electrolytes. However, the high ion concentration of water-in-salt electrolytes means that these systems are poorly understood when compared to more dilute electrolyte solutions. Here, we present direct surface force measurements across thin films of a water-in-salt electrolyte at several concentrations. We find that the electrolyte adopts a layered structure at charged interfaces composed of a nanostructure of a hydrated cation and nonaqueous anion-rich domains. These observations will aid in the interpretation of capacitance and double-layer behavior of water-in-salt electrolytes with consequences for their use in energy storage devices.

Nuclear magnetic resonance spin-lattice relaxation of lithium ions in aqueous solution by NMR and molecular dynamics

We study the aqueous solvation dynamics of lithium ions using nuclear magnetic resonance spectroscopy, molecular dynamics, and viscosity measurements. Several relaxation mechanisms are examined to explain the strong increases of spin-lattice relaxation toward high concentrations. The use of both ⁶Li and ⁷Li isotopes is helpful to identify the quadrupolar contribution to the relaxation rate. In particular, it is found that the quadrupolar interaction constitutes the strongest contribution above a concentration of ∼10 molal. The next-strongest contribution arises from interactions that scale with the square of the gyromagnetic ratio (mostly the dipolar interaction), and the experimental relaxation rates appear to be fully accounted for when these mechanisms are combined over the concentration range up to the saturation concentration. The study of solvation dynamics, particularly at high concentrations, could be of relevance for electrolyte dynamics in aqueous Li-ion rechargeable batteries.

Hydration structure and water exchange kinetics at xenotime-water interfaces: implications for rare earth minerals separation

Hydration of surface ions gives rise to structural heterogeneity and variable exchange kinetics of water at complex mineral-water interfaces. Here, we employ ab initio molecular dynamics (AIMD) simulations and water adsorption calorimetry to examine the aqueous interfaces of xenotime, a phosphate mineral that contains predominantly Y3+ and heavy rare earth elements. Consistent with natural crystal morphology, xenotime is predicted to have a tetragonal prismatic shape, dominated by the {100} surface. Hydration of this surface induces multilayer interfacial water structures with distinct OH orientations, which agrees with recent crystal truncation rod measurements. The exchange kinetics between two adjacent water layers exhibits a wide range of underlying timescales (5-180 picoseconds), dictated by ion-water electrostatics. Adsorption of a bidentate hydroxamate ligand reveals that {100} xenotime surface can only accommodate monodentate coordination with water exchange kinetics strongly depending on specific ligand orientation, prompting us to reconsider traditional strategies for selective separation of rare-earth minerals.

Hydration Mimicry by Membrane Ion Channels

Ions transiting biomembranes might pass readily from water through ion-specific membrane proteins if these protein channels provide environments similar to the aqueous solution hydration environment. Indeed, bulk aqueous solution is an important reference condition for the ion permeation process. Assessment of this hydration mimicry concept depends on understanding the hydration structure and free energies of metal ions in water in order to provide a comparison for the membrane channel environment. To refine these considerations, we review local hydration structures of ions in bulk water and the molecular quasi-chemical theory that provides hydration free energies. In doing so, we note some current views of ion binding to membrane channels and suggest new physical chemical calculations and experiments that might further clarify the hydration mimicry concept.

Structures and dynamic properties of the LiPF6 electrolytic solution under electric fields - a theoretical study

Fluorinated carbonates have attracted increasing attention in high-voltage lithium ion battery applications. Under free and electric fields, their structure-related solvent dynamic properties such as charge and discharge rate, however, are rarely reported. Herein, solutions including linear fluorinated carbonates have been simulated using joint MD/DFT calculations. For the first time, the dielectric constants of the four pure fluorinated carbonates have been predicted to be ca. 5.4 (4: ethyl-2,2,2-trifluoroethyl carbonate)-12.1 (7: di-1,1,2,2,2-pentafluoroethyl carbonate), which are dependent on the number of fluorine atoms. Minor difference in the solvation free energies and few contact ion associations were observed in the ETFEC and DTFEC solvents. Their comparable viscosity values were found through calculations of ion diffusivity and conductivity. In the electric fields, the Li⁺ mobilities in the two solutions have similar values, showing that the dynamic properties of the electrolytic solutions are almost independent of the number of fluorine atoms on these carbonates. There emerges an oriented and ordered arrangement of the solvent molecules and thus the largely decreased dielectric constants under the electric fields, even though the field strength is very low. These interesting phenomena should be relevant in the formation of contact and aggregate ion pairs, leading to unexpected reduction of the charge-discharge rate-related ion mobility in mixed solvents.

Solvation Structure of Li+ in Methanol and 2-Propanol Solutions Studied by ATR-IR and Neutron Diffraction with 6Li/7Li Isotopic Substitution Methods

Neutron diffraction measurements have been carried out on 10 mol % LiTFSA (TFSA: bis(trifluoromethylsulfonil)amide) solutions in methanol- d₄ and 2-propanol- d₈ to obtain information on the solvation structure of Li⁺. The detailed coordination structure of solvent molecules within the first solvation shell of Li⁺ was determined through the least-squares fitting analysis of the difference function between normalized scattering cross sections observed for ⁶Li/⁷Li isotopically substituted sample solutions. The nearest-neighbor Li⁺···O distance and coordination number determined for the 10 mol % LiTFSA-methanol- d₄ solution are r_LiO = 1.98 ± 0.02 Å and n_LiO = 3.8 ± 0.6, respectively. In the 2-propanol- d₈ solution, it has been revealed that 2-propanol- d₈ molecules within the first solvation shell of Li⁺ take at least two different coordination geometries with the intermolecular nearest-neighbor Li⁺···O distance of r_LiO = 1.93 ± 0.04 Å. The Li⁺···O coordination number, n_LiO = 3.3 ± 0.3, is determined. Ion-pair formation in the LiTFSA-methanol and LiTFSA-2-propanol solutions has been investigated by the attenuated total reflection infrared spectroscopic method. Mole fractions of free, Li⁺-bound, and aggregated TFSA^- are derived from the peak deconvolution analysis of vibrational bands observed for TFSA^-.

Ab Initio Molecular Dynamics Simulations of the Influence of Lithium Bromide on the Structure of the Aqueous Solution-Air Interface

We present the results of ab initio molecular dynamics simulations of the solution–air interface of aqueous lithium bromide (LiBr). We find that, in agreement with the experimental data and previous simulation results with empirical polarizable force field models, Br^– anions prefer to accumulate just below the first molecular water layer near the interface, whereas Li⁺ cations remain deeply buried several molecular layers from the interface, even at very high concentration. The separation of ions has a profound effect on the average orientation of water molecules in the vicinity of the interface. We also find that the hydration number of Li⁺ cations in the center of the slab N_{c,Li⁺–H2O} ≈ 4.7 ± 0.3, regardless of the salt concentration. This estimate is consistent with the recent experimental neutron scattering data, confirming that results from nonpolarizable empirical models, which consistently predict tetrahedral coordination of Li⁺ to four solvent molecules, are incorrect. Consequently, disruption of the hydrogen bond network caused by Li⁺ may be overestimated in nonpolarizable empirical models. Overall, our results suggest that empirical models, in particular nonpolarizable models, may not capture all of the properties of the solution–air interface necessary to fully understand the interfacial chemistry.

Quasi-Chemical Theory with Cluster Sampling from Ab Initio Molecular Dynamics: Fluoride (F-) Anion Hydration

Accurate predictions of the hydration free energy for anions typically has been more challenging than that for cations. Hydrogen bond donation to the anion in hydrated clusters such as F(H₂O) _n ^- can lead to delicate structures. Consequently, the energy landscape contains many local minima, even for small clusters, and these minima present a challenge for computational optimization. Utilization of cluster experimental results for the free energies of gas-phase clusters shows that even though anharmonic effects are interesting they need not be of troublesome magnitudes for careful applications of quasi-chemical theory to ion hydration. Energy-optimized cluster structures for anions can leave the central ion highly exposed, and application of implicit solvation models to these structures can incur more serious errors than those for metal cations. Utilizing cluster structures sampled from ab initio molecular dynamics simulations substantially fixes those issues.

Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li+ Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations

A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy Δ_s G_M⁺,wat^◦ of the Li⁺ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy [Formula: see text] of the proton, the surface electric potential jump χ_wat^◦ upon entering bulk water, and the absolute single-electrode potential [Formula: see text] of the reference hydrogen electrode are calculated to be -1099.9 ± 4.2 kJ·mol^-1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (-1100 ± 5 kJ·mol^-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li⁺ are also compared to those for Na⁺ and K⁺ from a previous study in terms of relative hydration free energies ΔΔ_s G_M⁺,wat^◦ and relative electrode potentials [Formula: see text]. The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔ_s G_M⁺,wat^• and redox potentials [Formula: see text]. The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller-Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li⁺ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.

Ion Hydration and Ion Pairing as Probed by THz Spectroscopy

Ion hydration is of pivotal importance for many fundamental processes. Various spectroscopic methods are used to study the retardation of the hydration bond dynamics in the vicinity of anions and cations. Here we introduce THz-FTIR spectroscopy as a powerful method to answer the open questions. We show through dissection of THz spectra that we can pinpoint characteristic absorption features that can be attributed to the rattling modes of strongly hydrating ions within their hydration cages as well as vibrationally induced charge fluctuations in the case of weakly hydrating ions. Further analysis yields information on anion-cation cooperativity, the size of the dynamic hydration shell, as well as the lifetimes of these collective ion-hydration water modes and their connecting thermal bath states. Our study provides evidence for a non-additive behavior, thus questioning the simplified Hofmeister model. THz spectroscopy enables ion pairing to be observed and quantified at a high salt concentration.

Strontium and barium in aqueous solution and a potassium channel binding site

Ion hydration structure and free energy establish criteria for understanding selective ion binding in potassium (K⁺) ion channels and may be significant to understanding blocking mechanisms as well. Recently, we investigated the hydration properties of Ba²⁺, the most potent blocker of K⁺ channels among the simple metal ions. Here, we use a similar method of combining ab initio molecular dynamics simulations, statistical mechanical theory, and electronic structure calculations to probe the fundamental hydration properties of Sr²⁺, which does not block bacterial K⁺ channels. The radial distribution of water around Sr²⁺ suggests a stable 8-fold geometry in the local hydration environment, similar to Ba²⁺. While the predicted hydration free energy of -331.8 kcal/mol is comparable with the experimental result of -334 kcal/mol, the value is significantly more favorable than the -305 kcal/mol hydration free energy of Ba²⁺. When placed in the innermost K⁺ channel blocking site, the solvation free energies and lowest energy structures of both Sr²⁺ and Ba²⁺ are nearly unchanged compared with their respective hydration properties. This result suggests that the block is not attributable to ion trapping due to +2 charge, and differences in blocking behavior arise due to free energies associated with the exchange of water ligands for channel ligands instead of free energies of transfer from water to the binding site.

Comparison of single-ion molecular dynamics in common solvents

Laying a basis for molecularly specific theory for the mobilities of ions in solutions of practical interest, we report a broad survey of velocity autocorrelation functions (VACFs) of Li⁺ and PF₆^- ions in water, ethylene carbonate, propylene carbonate, and acetonitrile solutions. We extract the memory function, γ(t), which characterizes the random forces governing the mobilities of ions. We provide comparisons controlling for the effects of electrolyte concentration and ion-pairing, van der Waals attractive interactions, and solvent molecular characteristics. For the heavier ion (PF₆^-), velocity relaxations are all similar: negative tail relaxations for the VACF and a clear second relaxation for γt, observed previously also for other molecular ions and with n-pentanol as the solvent. For the light Li⁺ ion, short time-scale oscillatory behavior masks simple, longer time-scale relaxation of γt. But the corresponding analysis of the solventberg Li⁺H₂O₄ does conform to the standard picture set by all the PF₆^- results.

Quasi-chemical theory of F-(aq): The "no split occupancies rule" revisited

We use ab initio molecular dynamics (AIMD) calculations and quasi-chemical theory (QCT) to study the inner-shell structure of F^-(aq) and to evaluate that single-ion free energy under standard conditions. Following the "no split occupancies" rule, QCT calculations yield a free energy value of -101 kcal/mol under these conditions, in encouraging agreement with tabulated values (-111 kcal/mol). The AIMD calculations served only to guide the definition of an effective inner-shell constraint. QCT naturally includes quantum mechanical effects that can be concerning in more primitive calculations, including electronic polarizability and induction, electron density transfer, electron correlation, molecular/atomic cooperative interactions generally, molecular flexibility, and zero-point motion. No direct assessment of the contribution of dispersion contributions to the internal energies has been attempted here, however. We anticipate that other aqueous halide ions might be treated successfully with QCT, provided that the structure of the underlying statistical mechanical theory is absorbed, i.e., that the "no split occupancies" rule is recognized.

Assessment of Simple Models for Molecular Simulation of Ethylene Carbonate and Propylene Carbonate as Solvents for Electrolyte Solutions

Progress in understanding liquid ethylene carbonate (EC) and propylene carbonate (PC) on the basis of molecular simulation, emphasizing simple models of interatomic forces, is reviewed. Results on the bulk liquids are examined from the perspective of anticipated applications to materials for electrical energy storage devices. Preliminary results on electrochemical double-layer capacitors based on carbon nanotube forests and on model solid-electrolyte interphase (SEI) layers of lithium ion batteries are considered as examples. The basic results discussed suggest that an empirically parameterized, non-polarizable force field can reproduce experimental structural, thermodynamic, and dielectric properties of EC and PC liquids with acceptable accuracy. More sophisticated force fields might include molecular polarizability and Buckingham-model description of inter-atomic overlap repulsions as extensions to Lennard-Jones models of van der Waals interactions. Simple approaches should be similarly successful also for applications to organic molecular ions in EC/PC solutions, but the important case of Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ deserves special attention because of the particularly strong interactions of that small ion with neighboring solvent molecules. To treat the Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ ions in liquid EC/PC solutions, we identify interaction models defined by empirically scaled partial charges for ion-solvent interactions. The empirical adjustments use more basic inputs, electronic structure calculations and ab initio molecular dynamics simulations, and also experimental results on Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ thermodynamics and transport in EC/PC solutions. Application of such models to the mechanism of Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ transport in glassy SEI models emphasizes the advantage of long time-scale molecular dynamics studies of these non-equilibrium materials.

Liquid Structure with Nano-Heterogeneity Promotes Cationic Transport in Concentrated Electrolytes

Using molecular dynamics simulations, small-angle neutron scattering, and a variety of spectroscopic techniques, we evaluated the ion solvation and transport behaviors in aqueous electrolytes containing bis(trifluoromethanesulfonyl)imide. We discovered that, at high salt concentrations (from 10 to 21 mol/kg), a disproportion of cation solvation occurs, leading to a liquid structure of heterogeneous domains with a characteristic length scale of 1 to 2 nm. This unusual nano-heterogeneity effectively decouples cations from the Coulombic traps of anions and provides a 3D percolating lithium-water network, via which 40% of the lithium cations are liberated for fast ion transport even in concentration ranges traditionally considered too viscous. Due to such percolation networks, superconcentrated aqueous electrolytes are characterized by a high lithium-transference number (0.73), which is key to supporting an assortment of battery chemistries at high rate. The in-depth understanding of this transport mechanism establishes guiding principles to the tailored design of future superconcentrated electrolyte systems.

A computational approach to calculate the heat of transport of aqueous solutions

Thermal gradients induce concentration gradients in alkali halide solutions, and the salt migrates towards hot or cold regions depending on the average temperature of the solution. This effect has been interpreted using the heat of transport, which provides a route to rationalize thermophoretic phenomena. Early theories provide estimates of the heat of transport at infinite dilution. These values are used to interpret thermodiffusion (Soret) and thermoelectric (Seebeck) effects. However, accessing heats of transport of individual ions at finite concentration remains an outstanding question both theoretically and experimentally. Here we discuss a computational approach to calculate heats of transport of aqueous solutions at finite concentrations, and apply our method to study lithium chloride solutions at concentrations >0.5 M. The heats of transport are significantly different for Li⁺ and Cl⁻ ions, unlike what is expected at infinite dilution. We find theoretical evidence for the existence of minima in the Soret coefficient of LiCl, where the magnitude of the heat of transport is maximized. The Seebeck coefficient obtained from the ionic heats of transport varies significantly with temperature and concentration. We identify thermodynamic conditions leading to a maximization of the thermoelectric response of aqueous solutions.

The role of ion–water interactions in determining the Soret coefficient of LiCl aqueous solutions

The solvation structure of Li⁺ plays a key role in determining the Soret coefficient of LiCl aqueous solutions.

Molecular Dynamics Study of Mg2+/Li+ Separation via Biomimetic Graphene-Based Nanopores: The Role of Dehydration in Second Shell

Residual Mg²⁺ reduces the performance of lithium-ion batteries. However, separating Mg²⁺ and Li⁺ is difficult because of their similar ionic properties. Inspired by the high selectivity of biological Mg²⁺ channels, this work utilizes atomistic simulations to investigate the ability of graphene-based nanopores with diameters of 0.789, 1.024, and 1.501 nm to separate Mg²⁺ and Li⁺ under a series of transmembrane voltages. We analyzed the spatial distribution of molecules in the nanopores' vicinity, structure properties of ionic hydration, and potential of mean force of ions traveling through the nanopores. Separation was mainly caused by the difference in dehydration between the second hydration shells of Mg²⁺ and Li⁺. When ions traveled through nanopores, Li⁺ had to overcome a greater energy barrier than Mg²⁺ because it had to shed more water molecules and break more hydrogen bonds in the second hydration shell compared with Mg²⁺. Moreover, the ionic Coulomb blockade of Mg²⁺ occurred near the pore mouth, impeding Li⁺ transport and increasing selectivity when the pore diameter decreased to subnanometer.

Ion-Specific Effects in Carboxylate Binding Sites

Specific ion binding by carboxylates (-COO^-) is a broadly important topic because -COO^- is one of the most common functional groups coordinated to metal ions in metalloproteins and synthetic polymers. We apply quantum chemical methods and the quasi-chemical free-energy theory to investigate how variations in the number of -COO^- ligands in a binding site determine ion-binding preferences. We study a series of monovalent (Li⁺, Na⁺, K⁺, Cs⁺) and divalent (Zn²⁺, Ca²⁺) ions relevant to experimental work on ion channels and ionomers. Of two competing hypotheses, our results support the ligand field strength hypothesis and follow the reverse Hofmeister series for ion solvation and ion transfer from aqueous solution to binding sites with the preferred number of ligands. New insight arises from the finding that ion-binding sequences can be manipulated and even reversed just by constraining the number of carboxylate ligands in the binding sites. Our results help clarify the discrepancy in ion association between molecular ligands in aqueous solutions and ionomers, and their chemical analogues in ion-channel binding sites.

Some physicochemical aspects of water-soluble mineral flotation

Some physicochemical aspects of water-soluble mineral flotation including hydration phenomena, associations and interactions between collectors, air bubbles, and water-soluble mineral particles are presented. Flotation carried out in saturated salt solutions, and a wide range of collector concentrations for effective flotation of different salts are two basic aspects of water-soluble mineral flotation. Hydration of salt ions, mineral particle surfaces, collector molecules or ions, and collector aggregates play an important role in water-soluble mineral flotation. The adsorption of collectors onto bubble surfaces is suggested to be the precondition for the association of mineral particles with bubbles. The association of collectors with water-soluble minerals is a complicated process, which may include the adsorption of collector molecules or ions onto such surfaces, and/or the attachment of collector precipitates or crystals onto the mineral surfaces. The interactions between the collectors and the minerals include electrostatic and hydrophobic interactions, hydrogen bonding, and specific interactions, with electrostatic and hydrophobic interactions being the common mechanisms. For the association of ionic collectors with minerals with an opposite charge, electrostatic and hydrophobic interactions could have a synergistic effect, with the hydrophobic interactions between the hydrophobic groups of the previously associated collectors and the hydrophobic groups of oncoming collectors being an important attractive force. Association between solid particles and air bubbles is the key to froth flotation, which is affected by hydrophobicity of the mineral particle surfaces, surface charges of mineral particles and bubbles, mineral particle size and shape, temperature, bubble size, etc. The use of a collector together with a frother and the use of mixed surfactants as collectors are suggested to improve flotation.

“Thought experiments” as dry-runs for “tough experiments”: novel approaches to the hydration behavior of oxyanions

We explore the deconvolution of correlations for the interpretation of the microstructural behavior of aqueous electrolytes according to the neutron diffraction with isotopic substitution (NDIS) approach toward the experimental determination of ion coordination numbers of systems involving oxyanions, in particular, sulfate anions. We discuss the alluded interplay in the title of this presentation, emphasized the expectations, and highlight the significance of tackling the challenging NDIS experiments. Specifically, we focus on the potential occurrence of $N{i^{2 + }} \cdots SO_4^{2 - }$ pair formation, identify its signature, suggest novel ways either for the direct probe of the contact ion pair (CIP) strength and the subsequent correction of its effects on the measured coordination numbers, or for the determination of anion coordination numbers free of CIP contributions through the implementation of null-cation environments. For that purpose we perform simulations of NiSO4 aqueous solutions at ambient conditions to generate the distribution functions required in the analysis (a) to identify the individual partial contributions to the total neutron-weighted distribution function, (b) to isolate and assess the contribution of $N{i^{2 + }} \cdots SO_4^{2 - }$ pair formation, (c) to test the accuracy of the neutron diffraction with isotope substitution based coordination calculations and X-ray diffraction based assumptions, and (d) to describe the water coordination around both the sulfur and oxygen sites of the sulfate anion. We finally discuss the strength of this interplay on the basis of the inherent molecular simulation ability to provide all pair correlation functions that fully characterize the system microstructure and allows us to “reconstruct” the eventual NDIS output, i.e., to take an atomistic “peek” (e.g., see Figure 1) at the local environment around the isotopically-labeled species before any experiment is ever attempted, and ultimately, to test the accuracy of the “measured” NDIS-based coordination numbers against the actual values by the “direct” counting.

Super-Maxwellian helium evaporation from pure and salty water

Helium atoms evaporate from pure water and salty solutions in super-Maxwellian speed distributions, as observed experimentally and modeled theoretically. The experiments are performed by monitoring the velocities of dissolved He atoms that evaporate from microjets of pure water at 252 K and 4-8.5 molal LiCl and LiBr at 232-252 K. The average He atom energies exceed the flux-weighted Maxwell-Boltzmann average of 2RT by 30% for pure water and 70% for 8.5m LiBr. Classical molecular dynamics simulations closely reproduce the observed speed distributions and provide microscopic insight into the forces that eject the He atoms from solution. Comparisons of the density profile and He kinetic energies across the water-vacuum interface indicate that the He atoms are accelerated by He-water collisions within the top 1-2 layers of the liquid. We also find that the average He atom kinetic energy scales with the free energy of solvation of this sparingly soluble gas. This free-energy difference reflects the steeply decreasing potential of mean force on the He atoms in the interfacial region, whose gradient is the repulsive force that tends to expel the atoms. The accompanying sharp decrease in water density suppresses the He-water collisions that would otherwise maintain a Maxwell-Boltzmann distribution, allowing the He atom to escape at high energies. Helium is especially affected by this reduction in collisions because its weak interactions make energy transfer inefficient.