Density functional theory based molecular dynamics study of solution composition effects on the solvation shell of metal ions

Ab Initio Simulation of Liquid Water without Artificial High Temperature

Comprehending the structure and dynamics of water is crucial in various fields, such as water desalination, ion separation, electrocatalysis, and biochemical processes. While reported works show that the ab initio molecular dynamics (AIMD) can accurately portray water's structure, the artificial high temperature (AHT) from 120 to 30 K is needed to mimic the quantum nature of hydrogen-bond network from GGA, metaGGA to hybrid functionals. The AHT proves to be an inadequate approach for systems involving aqueous multiphase mixtures, such as water-solid interfaces and aqueous solutions. This is due to the activation of additional phonons in other phases, which can lead to an overestimation of the dynamics of nearby water molecules. In this work, we find that the regularized SCAN (rSCAN) functional effectively captures both the structure and dynamics of liquid water at ambient conditions without AHT. Moreover, rSCAN closely matches experimental results for the hydration structures of alkali, alkali earth, and halide ions. We anticipate that the versatile and accurate rSCAN functional will emerge as a key tool based on ab initio simulation for investigating chemical processes in aqueous environments.

Kinetics of Calcite Nucleation onto Sulfated Chitosan Derivatives and Implications for Water-Polysaccharide Interactions during Crystallization of Sparingly Soluble Salts

Anionic macromolecules are found at sites of CaCO3 biomineralization in diverse organisms, but their roles in crystallization are not well-understood. We prepared a series of sulfated chitosan derivatives with varied positions and degrees of sulfation, DS(SO3 -), and measured calcite nucleation rate onto these materials. Fitting the classical nucleation theory model to the kinetic data reveals the interfacial free energy of the calcite-polysaccharide-solution system, γnet, is lowest for nonsulfated controls and increases with DS(SO3 -). The kinetic prefactor also increases with DS(SO3 -). Simulations of Ca2+-H2O-chitosan systems show greater water structuring around sulfate groups compared to uncharged substituents, independent of sulfate location. Ca2+-SO3 - interactions are solvent-separated by distances that are inversely correlated with DS(SO3 -) of the polysaccharide. The simulations also predict SO3 - and NH3 + groups affect the solvation waters and HCO3 - ions associated with Ca2+. Integrating the experimental and computational evidence suggests sulfate groups influence nucleation by increasing the difficulty of displacing near-surface water, thereby increasing γnet. By correlating γnet and net charge per monosaccharide for diverse polysaccharides, we suggest the solvent-separated interactions of functional groups with Ca2+ influence thermodynamic and kinetic components to crystallization by similar solvent-dominated processes. The findings reiterate the importance of establishing water structure and properties at macromolecule-solution interfaces.

Mechanistic Insights into N2O5-Halide Ions Chemistry at the Air-Water Interface

The activation of halogens (X = Cl, Br, I) by N2O5 is linked to NOx sources, ozone concentrations, NO3 reactivity, and the chemistry of halide-containing aerosol particles. However, a detailed chemical mechanism is still lacking. Herein, we explored the chemistry of the N2O5···X- systems at the air-water interface. Two different reaction pathways were identified for the reaction of N2O5 with X- at the air-water interface: the formation of XNO2 or XONO, along with NO3-. In the case of the Cl- system, the ClNO2 generation pathway is more favorable, while for the Br- and I- systems, the formation of BrONO and IONO is barrierless, making them the predominant products. Furthermore, the mechanisms of formation of X2 from XNO2 and XONO were also investigated. The high energy barriers of reactions and the high free energies of the products compared to those of the reactants indicate that ClNO2 is stable at the air-water interface. Contrary to the widely held belief regarding X2 producing from the reaction of XNO2 with X-, our calculations demonstrate that BrONO and IONO initially form stable BrONO···Br- and IONO···I- complexes, which then subsequently react with Br- and I- to form Br3- and I3-, respectively. Finally, Br3- and I3- decompose to form Br2 and I2. These findings have significant implications for experimental interpretation and offer new insights into halogen cycling in the atmosphere.

Ion-Specific Effects on Ion and Polyelectrolyte Solvation

Ion-specific effects on aqueous solvation of monovalent counter ions, Na+ ${^+ }$ , K+ ${^+ }$ , Cl- ${^- }$ , and Br- ${^- }$ , and two model polyelectrolytes (PEs), poly(styrene sulfonate) (PSS) and poly(diallyldimethylammonium) (PDADMA) were here studied with ab initio molecular dynamics (AIMD) and classical molecular dynamics (MD) simulations based on the OPLS-aa force-field which is an empirical fixed point-charge force-field. Ion-specific binding to the PE charge groups was also characterized. Both computational methods predict similar response for the solvation of the PEs but differ notably in description of ion solvation. Notably, AIMD captures the experimentally observed differences in Cl- ${^- }$ and Br- ${^- }$ anion solvation and binding with the PEs, while the classical MD simulations fail to differentiate the ion species response. Furthermore, the findings show that combining AIMD with the computationally less costly classical MD simulations allows benefiting from both the increased accuracy and statistics reach.

Potassium adsorption capacity and desorption kinetics in soils of Qenberenaweti sub-watershed, central highlands of Ethiopia

Determining the supply and uptake of K nutrient and the dynamic equilibrium (adsorption-desorption) reactions among the K forms in the soils are not commonly addressed in the highlands of Ethiopia. A study was therefore initiated to determine the adsorption capacity of the exchangeable K and the release kinetics of the non-exchangeable K in the soils of the Qenberenaweti Sub-watershed. Twelve disturbed surface (0-20 cm) soil sub-samples were collected from every farmland which was representative of each pre-identified soil type (Vertic Cambisols, Pellic Vertisols, Pisoplinthic Luvisols, Relictistagnic Cambisols, Pisoplinthic Cambisols, and Plinthofractic Cambisols). A composite sample was made in duplicate for the determination of K adsorption capacity and desorption kinetics per soil type. The mean maximum (69.47 ± 4.31 %) and minimum (56.16 ± 6.04 %) K adsorption rates were obtained from the Plinthofractic Cambisols and Vertic Cambisols, respectively. Among the tested isotherm models, the goodness of the Freundlich was better fit the data of all experimental soils; hence, a modified equation of this model (qe = aCeb/a) could be used to describe the theoretical doses of K fertilizers required to develop K levels in soil solutions. The highest constant K releases from the Plinthofractic Cambisols (47 mg kg-1), Pisiopllintic Cambisols (46 mg kg-1), and Pisoplinthic Luvisols (44 mg kg-1) were attained at the 9th extraction. In comparison, it was noticed at the 7th and 11th extractions of the Relictistagnic Cambisols (45 mg kg-1) and both Pellic Vertisols (48 mg kg-1) and Vertic Cambisols (42 mg kg-1), respectively. The equation of power function was the best to successfully describe the released K+ from all the experimental soils. Eventually, determining the adsorption capacity and release kinetics of K at a site-specific level helps to know the relative potential of the soils to supply K and also plan for an effective K fertilization strategy.

Fast Structural Dynamics in Concentrated HCl Solutions: From Proton Hopping to the Bulk Viscosity

Concentrated acid solutions, particularly HCl, have been studied extensively to examine the proton hopping and infrared spectral signatures of hydronium ions. Much less attention has been given to the structural dynamics of concentrated HCl solutions. Here, we apply optical heterodyne detected-optical Kerr effect (OHD-OKE) measurements to examine HCl concentration-dependent dynamics from moderate (0.8 m) to very high (15.5 m) concentrations and compare the results to the dynamics of NaCl solutions, as Na+ is similar in size to the hydronium cation. Both HCl and NaCl OHD-OKE signals decay as triexponentials at all concentrations, in contrast to pure water, which decays as a biexponential. Two remarkable features of the HCl dynamics are the following: (1) the bulk viscosity is linearly related to the slowest decay constant, t3, and (2) the concentration-dependent proton hopping times, determined by ab initio MD simulations and 2D IR chemical exchange experiments, both obtained from the literature, fall on the same line as the slowest structural dynamics relaxation time, t3, within experimental error. The structural dynamics of hydronium/chloride/water clusters, with relaxation times t3, are responsible for the concentration dependence of microscopic property of proton hopping and the macroscopic bulk viscosity. The slowest time constant (t3), which does not have a counterpart in pure water, is 3 ps at 0.8 m and increases by a factor of ∼2 by 15.5 m. The two fastest HCl decay constants, t1 and t2, are similar to those of pure water and increase mildly with the concentration.

On Local Structure Equilibration of Ca2+ in Solution by Ab Initio Molecular Dynamics

Analyzing the stable isotopic ratio of Ca offers valuable insights into a wide range of applications from climate reconstruction to bone cancer diagnosis and agricultural nutrient improvement. While the first hydration shell of Ca in solution is expected to play a major role in its fractionation properties, the coordination of Ca in water remains a subject of debate. In this work, Ca2+ in water has been modeled by means of ab initio molecular dynamics simulations using various exchange and correlation functionals and at different temperatures. Results show a significant effect of the functional on the average Ca2+ coordination, depending on its tendency to over- or understructure liquid water. The BLYP functional with Grimme-D2 correction was judged as the most accurate among those tested based on its accuracy to reproduce water structural and diffusion properties. Using this functional, the effect of temperature has been systematically investigated, focusing on means to limit the uncertainty in our assessments of the average coordination of Ca2+ ions by (1) estimating the number of water exchanges in the simulations and (2) implementing a statistical approach based on Markov chains. The findings indicate, especially, that our simulations at 300, 350, and 400 K do not yield converged results due to potential equilibration problems. These observations impose substantial constraints on the trustworthiness of numerous estimates in the existing literature that depend on trajectories with insufficient exchanges. We estimate Ca2+ coordination values of 6.8 ± 0.1, 6.8 ± 0.1, 6.7 ± 0.2, and 6.7 ± 0.2 at 600, 550, 500, and 450 K respectively. At lower temperatures (300, 350, and 400 K), while obtaining definitive values for Ca2+ coordination remains challenging, our research does indicate a potential temperature-related influence on coordination with an average Ca2+ coordination at 300 K as low as 6.2.

Boron-containing fullerene-based salts with cyclic carbonate solvents as electrolytes for Li-ion batteries and beyond

Replacement of carbon atoms by a heteroatom in fullerene is a promising route that enhances the electronic properties of fullerenes and results in hetero fullerene-based effective agents ensuring applications in vivid fields of the solar cell, cathode materials for batteries, etc. Towards the development of new electrolyte salts, attention has been paid to facilitating ion mobility in particular and moderate stability of the anions in addition. From the atomistic molecular dynamics simulation studies, for the first time, we uncover that the boron-containing hetero fullerene, C59B- anion-based LiC59B, and NaC59B salts in cyclic carbonate solvents can act as efficient electrolytes by improving the transport phenomenon of the metal ions in solution, importantly for Li+ and satisfactorily for Na+ as compared to their commonly used BF4- anion based salts. Additionally, our study revealed that apart from LiC59B, and NaC59B salts, C58B22- based MgC58B2 salt can facilitate the ionic conductivity of the electrolyte. The properties of the proposed electrolyte under an electric field and different temperatures were investigated. Some of the bulk properties of the used electrolytes to some extent were found to be improved in the presence of these salts. The first principle-based electrochemical calculations further justify the stability of the proposed anions. The initial investigation from the Reactive force-field (ReaxFF) based atomistic simulations study elucidates that LiC59B reduces the decomposition of the EC solvent compared to LiBF4 and facilitates solvent stability.

Consistent density functional theory-based description of ion hydration through density-corrected many-body representations

Delocalization error constrains the accuracy of density functional theory in describing molecular interactions in ion-water systems. Using Na+ and Cl- in water as model systems, we calculate the effects of delocalization error in the SCAN functional for describing ion-water and water-water interactions in hydrated ions, and demonstrate that density-corrected SCAN (DC-SCAN) predicts n-body and interaction energies with an accuracy approaching coupled cluster theory. The performance of DC-SCAN is size-consistent, maintaining an accurate description of molecular interactions well beyond the first solvation shell. Molecular dynamics simulations at ambient conditions with many-body MB-SCAN(DC) potentials, derived from the many-body expansion, predict the solvation structure of Na+ and Cl- in quantitative agreement with reference data, while simultaneously reproducing the structure of liquid water. Beyond rationalizing the accuracy of density-corrected models of ion hydration, our findings suggest that our unified density-corrected MB formalism holds great promise for efficient DFT-based simulations of condensed-phase systems with chemical accuracy.

Transition metal doped WSi2N4monolayer for water splitting electrocatalysts: a first-principles study

High-performance water splitting electrocatalysts are urgently needed in the face of the environmental degradation and energy crisis. The first principles method was used in this study to systematically examine the electronic characteristics of transition metal (Sc, Ti, V, Cr, Mn, Fe, and Ru) doped WSi2N4(TM@WSi2N4) and its potential as oxygen evolution reaction (OER) catalysts. Our study shows that the doping of TM atoms significantly improves the catalytic performance of TM@WSi2N4, especially Fe@WSi2N4shows a low overpotential (ηOER= 470 mV). Interestingly, we found that integrated-crystal orbital Hamilton population and d-band center can be used as descriptors to explain the high catalytic activity of Fe@WSi2N4. Subsequently, Fe@WSi2N4exhibits the best hydrogen evolution reaction (HER) activity with a universal overpotential of 47 mV on N1sites. According to our research, Fe@WSi2N4offers a promising substitute for precious metals as a catalyst for overall water splitting with low OER and HER overpotentials.

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.

Short-Range Cooperative Slow-down of Water Solvation Dynamics Around SO4 2--Mg2+ Ion Pairs

The presence of ions affects the structure and dynamics of water on a multitude of length and time scales. In this context, pairs of Mg²⁺ and SO₄ ^2- ions in water constitute a prototypical system for which conflicting pictures of hydration geometries and dynamics have been reported. Key issues are the molecular pair and solvation shell geometries, the spatial range of electric interactions, and their impact on solvation dynamics. Here, we introduce asymmetric SO₄ ^2- stretching vibrations as new and most specific local probes of solvation dynamics that allow to access ion hydration dynamics at the dilute concentration (0.2 M) of a native electrolyte environment. Highly sensitive heterodyne 2D-IR spectroscopy in the fingerprint region of the SO₄ ^2- ions around 1100 cm^-1 reveals a specific slow-down of solvation dynamics for hydrated MgSO₄ and for Na₂SO₄ in the presence of Mg²⁺ ions, which manifests as a retardation of spectral diffusion compared to aqueous Na₂SO₄ solutions in the absence of Mg²⁺ ions. Extensive molecular dynamics and density functional theory QM/MM simulations provide a microscopic view of the observed ultrafast dephasing and hydration dynamics. They suggest a molecular picture where the slow-down of hydration dynamics arises from the structural peculiarities of solvent-shared SO₄ ^2--Mg²⁺ ion pairs.

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.

Quantum chemical investigation of the effect of alkali metal ions on the dynamic structure of water in aqueous solutions

We report quantum chemical molecular dynamics (MD) simulations based on the density-functional tight-binding (DFTB) method to investigate the effect of K+, Na+, and Mg2+ ions in aqueous solutions on the static and dynamic structure of bulk water at room temperature and with various concentrations. The DFTB/MD simulations were validated for the description of ion solvation in aqueous ionic solutions by comparing static pair distribution functions (PDFs) as well as the cation solvation shell between experimental and available ab initio DFT data. The effect of the cations on the water structure, as well as relative differences between K+, Na+, and Mg2+ cations, were analyzed in terms of atomically resolved PDFs as well as time-dependent Van Hove correlation functions (VHFs). The investigation of the VHFs reveals that salt ions generally slow down the dynamic decay of the pair correlations in the water solvation sphere, irrespective of the cation size or charge. The analysis of partial metal-oxygen VHFs indicates that there are long-lived correlations between water and Na+ over long distances, in contrast to K+ and Mg2+.

Adsorption of 4-Mercapto Pyridine with Gold Nanoparticles Embedded in the Langmuir-Blodgett Film Matrix of Stearic Acid: SERS, XPS Studies Aided by Born-Oppenheimer on the Fly Dynamics, Time-Resolved Wavelet Transform Theory, and DFT

This paper reports the adsorptive behavior of the 4-mercaptopyridine (4MPy) molecule soaked in gold nanoparticles (AuNPs) that remain embedded in the bilayer Langmuir-Blodgett (LB) film matrix of stearic acid (SA) for various soaking times (STs). The as-fabricated substrate proved to be an efficient SERS sensing platform that can sense the analyte 4MPy molecules at trace concentrations of ∼1.0 × 10-9 M. The XPS study not only reveals the adsorption of 4Mpy molecules with AuNPs via a sulfur atom but also suggests partial degradation of the analyte molecule upon adsorption. This observation is further substantiated from the SERS spectral profile, which shows unusual broadening of the enhanced Raman bands of the molecule at higher STs. The experimental observations are supported by Born-Oppenheimer on-the-fly molecular dynamics (BO-OF-MD), time-resolved wavelet transform theory (WT), and the DFT calculations based on adcluster models. Selective enhancements of Raman bands in the SERS spectra further suggest the involvement of charge transfer (CT) interaction to the overall enhancements of Raman bands of the analyte molecule. The molecule → CT contribution has been estimated from electron density difference calculations and the corresponding CT distance; the amount of CT is also envisaged.

Conductivity Mechanism in Ionic 2D Carbon Nitrides: From Hydrated Ion Motion to Enhanced Photocatalysis

Carbon nitrides are among the most studied materials for photocatalysis; however, limitations arise from inefficient charge separation and transport within the material. Here, this aspect is addressed in the 2D carbon nitride poly(heptazine imide) (PHI) by investigating the influence of various counterions, such as M = Li⁺ , Na⁺ , K⁺ , Cs⁺ , Ba²⁺ , NH₄ ⁺ , and tetramethyl ammonium, on the material's conductivity and photocatalytic activity. These ions in the PHI pores affect the stacking of the 2D layers, which further influences the predominantly ionic conductivity in M-PHI. Na-containing PHI outperforms the other M-PHIs in various relative humidity (RH) environments (0-42%RH) in terms of conductivity, likely due to pore-channel geometry and size of the (hydrated) ion. With increasing RH, the ionic conductivity increases by 4-5 orders of magnitude (for Na-PHI up to 10^-5 S cm^-1 at 42%RH). At the same time, the highest photocatalytic hydrogen evolution rate is observed for Na-PHI, which is mirrored by increased photogenerated charge-carrier lifetimes, pointing to efficient charge-carrier stabilization by, e.g., mobile ions. These results indicate that also ionic conductivity is an important parameter that can influence the photocatalytic activity. Besides, RH-dependent ionic conductivity is of high interest for separators, membranes, or sensors.

Sulfate and Molybdate Incorporation at the Calcite-Water Interface: Insights from Ab Initio Molecular Dynamics

Sulfur and molybdenum trace impurities in speleothems (stalagmites and stalactites) can provide long and continuous records of volcanic activity, which are important for past climatic and environmental reconstructions. However, the chemistry governing the incorporation of the trace element-bearing species into the calcium carbonate phases forming speleothems is not well understood. Our previous work has shown that substitution of tetrahedral oxyanions [XO4]2- (X = S and Mo) replacing [CO3]2- in CaCO3 bulk phases (except perhaps for vaterite) is thermodynamically unfavorable with respect to the formation of competing phases, due to the larger size and different shape of the [XO4]2- tetrahedral anions in comparison with the flat [CO3]2- anions, which implied that most of the incorporation would happen at the surface rather than at the bulk of the mineral. Here, we present an ab initio molecular dynamics study, exploring the incorporation of these impurities at the mineral-water interface. We show that the oxyanion substitution at the aqueous calcite (10.4) surface is clearly favored over bulk incorporation, due to the lower structural strain on the calcium carbonate solid. Incorporation at surface step sites is even more favorable for both oxyanions, thanks to the additional interface space afforded by the surface line defect to accommodate the tetrahedral anion. Differences between sulfate and molybdate substitutions can be mostly explained by the size of the anions. The molybdate oxyanion is more difficult to incorporate in the calcite bulk than the smaller sulfate oxyanion. However, when molybdate is substituted at the surface, the elastic cost is avoided because the oxyanion protrudes out of the surface and gains stability via the interaction with water at the interface, which in balance results in more favorable surface substitution for molybdate than for sulfate. The detailed molecular-level insights provided by our calculations will be useful to understand the chemical basis of S- and Mo-based speleothem records.

Dynamic ionic radius of alkali metal ions in aqueous solution: a pulsed-field gradient NMR study

The dynamic behavior of alkali metal ions, Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺ in aqueous solutions is one of the most important topics in solution chemistry. Since these alkali metals contain nuclear magnetic resonance (NMR) active nuclei, it is possible to directly measure the diffusion constants of the alkali metal ions using the pulsed field gradient (PFG) NMR method. In this paper, the ⁷Li, ²³Na, ⁸⁷Rb, ¹³³Cs and ¹H resonances are observed for diffusion constants in aqueous solution and the solvent H₂O. Until now, the values of the diffusion constant have been lacking when discussing hydration effects around alkali metal ions. It is known that the static ionic radius (R_ion) increases with increasing the atomic number, and the experimental diffusion constants also increase with increasing the atomic number, which is opposite to the Stokes–Einstein (SE) relation. It suggests that alkali metal ions diffuse through a space of 10⁻⁶ m accompanying the hydrated spheres with a time interval of 10⁻³ s. For each alkali metal ion, the dynamic ionic radius is evaluated.

Stokes radius (dynamic ionic radius) of the alkali metal ions versus the ionic radius (R_ion) at 303 K. The dotted line is a guide for the 1 : 1 relation.

Confinement effects on the solvation structure of solvated alkaline metal cations in a single-digit 1T-MoS2 nanochannel: A first-principles study

Confinement plays an important role in determining ion transport in porous materials, which, in turn, may influence the performance of many energy storage and desalination devices. In this work, we combined density functional theory (DFT) with an implicit solvation model and ab initio molecular dynamics (AIMD) to investigate the effects of nanoconfinement on several solvated alkaline metal cations in a single-digit 1T-MoS₂ nanochannel. Our DFT calculations with a solvation model indicated that cations with stronger hydration energy introduce a higher number of co-intercalated water molecules into the channel, consistent with early experimental observation obtained for MXene (2D transition metal carbide) channels. The predicted optimal water numbers for the cations were then used for AIMD simulations that explicitly include the effects of the solvent. When compared with the cations in bulk solution, our simulations showed that the hydration structure and coordination number (CN) of the solvated cations confined in the MoS₂ channel can be significantly altered. We found that larger cations with weaker hydration energy (K⁺, Rb⁺, and Cs⁺) exhibited a distinctive CN decrease under confinement, while smaller cations (Li⁺ and Na⁺) retained a similar hydration shell as in the bulk solution. More specifically, the hydration shell of large cations (K⁺, Rb⁺, and Cs⁺) in MoS₂ showed similar features of the coordination angle to the bulk, which suggests the partially broken hydration shell with no geometry change under confinement. Our simulations provided insights into the change of the hydration structure of alkaline metal cations under confinement, which may have important implications on their transport in the 1T-MoS₂ channel.

Assessing the Intrinsic Strengths of Ion–Solvent and Solvent–Solvent Interactions for Hydrated Mg2+ Clusters

Information resulting from a comprehensive investigation into the intrinsic strengths of hydrated divalent magnesium clusters is useful for elucidating the role of aqueous solvents on the Mg2+ ion, which can be related to those in bulk aqueous solution. However, the intrinsic Mg–O and intermolecular hydrogen bond interactions of hydrated magnesium ion clusters have yet to be quantitatively measured. In this work, we investigated a set of 17 hydrated divalent magnesium clusters by means of local vibrational mode force constants calculated at the ωB97X-D/6-311++G(d,p) level of theory, where the nature of the ion–solvent and solvent–solvent interactions were interpreted from topological electron density analysis and natural population analysis. We found the intrinsic strength of inner shell Mg–O interactions for [Mg(H2O)n]2+ (n = 1–6) clusters to relate to the electron density at the bond critical point in Mg–O bonds. From the application of a secondary hydration shell to [Mg(H2O)n]2+ (n = 5–6) clusters, stronger Mg–O interactions were observed to correspond to larger instances of charge transfer between the lp(O) orbitals of the inner hydration shell and the unfilled valence shell of Mg. As the charge transfer between water molecules of the first and second solvent shell increased, so did the strength of their intermolecular hydrogen bonds (HBs). Cumulative local vibrational mode force constants of explicitly solvated Mg2+, having an outer hydration shell, reveal a CN of 5, rather than a CN of 6, to yield slightly more stable configurations in some instances. However, the cumulative local mode stretching force constants of implicitly solvated Mg2+ show the six-coordinated cluster to be the most stable. These results show that such intrinsic bond strength measures for Mg–O and HBs offer an effective way for determining the coordination number of hydrated magnesium ion clusters.