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

Improving pKa Predictions with Reparameterized Force Fields and Free Energy Calculations

Given the growing interest in designing targeted covalent inhibitors, methods for rapidly and accurately probing pKas─and, by extension, the reactivities─of target cysteines are highly desirable. Complementary to cysteine, histidine is similarly relevant due to its frequent presence in protein active sites and its unique ability to exist in two tautomeric states. Here, we demonstrate that nonequilibrium free energy calculations can accurately determine the pKa values of both residues, often outperforming conventional predictors. Importantly, we find that (1) increasing the van der Waals radius of cysteine's sulfur atom, (2) modifying the backbone charges of histidine, and (3) introducing effective polarization by downscaling the side chain partial charges of both residues can all significantly improve pKa prediction accuracy. Using the modified CHARMM36m force field on the full dataset reduces the prediction error from 2.12 ± 0.27 pK to 1.28 ± 0.15 pK and increases the correlation with experiment from 0.25 ± 0.09 to 0.58 ± 0.08. Similarly, using the modified Amber14SB force field decreases the error from 3.21 ± 0.29 pK to 1.69 ± 0.23 pK and improves the correlation from 0.15 ± 0.10 to 0.36 ± 0.10.

Shadow Molecular Dynamics with a Machine Learned Flexible Charge Potential

We present an extended Lagrangian shadow molecular dynamics scheme with an interatomic Born-Oppenheimer potential determined by the relaxed atomic charges of a second-order charge equilibration model. To parametrize the charge equilibration model, we use machine learning with neural networks to determine the environment-dependent electronegativities and chemical hardness parameters for each atom, in addition to the charge-independent energy and force terms. The approximate shadow molecular dynamics potential in combination with the extended Lagrangian formulation improves the numerical stability and reduces the number of Coulomb potential calculations required to evaluate accurate conservative forces. We demonstrate efficient and accurate simulations with excellent long-term stability of the molecular dynamics trajectories. The significance of choosing fixed or environment-dependent electronegativities and chemical hardness parameters is evaluated. Finally, we compute the infrared spectrum of molecules via the dipole autocorrelation function and compare to experiments to highlight the accuracy of the shadow molecular dynamics scheme with a machine learned flexible charge potential.

Polarizable potential window at soft molecular interfaces as a quantitative descriptor for the water content in organic solvents

The presence of water in organic solvents is a ubiquitous fact and can affect the reactivity and selectivity of chemical reactions. Traditional physical and chemical methods (IR, NMR, Karl Fischer titration, etc.) for quantitative measurement of water in organic solvents are not very suitable for rapid trace water analysis. Here, we demonstrate that, with hydrated Li+ and Cl- as probes to build polarizable potential windows (PPWs) at interfaces between water and more than twenty organic solvents, we can reflect the water content in organic solvents. This method only requires a scan of a cyclic voltammogram for Li+ and Cl- transfer (a weak-interaction electrochemical method), at a micro-scale polarized water/oil interface. A hybrid modified Born ionic solvation model was employed by us to compute the theoretical PPWs of LiCl at a series of water/oil interfaces, which match with the experimental results to some extent. Experiments and theories jointly confirm a novel and universal relationship: the PPW width correlates with the water content (in a large range) in organic solvents in a negative natural logarithm way. We postulate that when the organic solvent is different, the water fingers, i.e., ions dragging a string of water molecules, will search for water molecules in the organic phase with different probabilities (or microstate numbers) after crossing the interface. This determines the macroscopic quantities, namely the standard Gibbs free energy of ion transfer and the PPW width. It is envisioned that our work paves the way for a broad spectrum of applications.

Computational Explorations of Th4+ First Hydrolysis Reaction Constants: Insights from Ab Initio Molecular Dynamics and Density Functional Theory Calculations

The fundamental hydrolysis behavior of tetravalent actinide cations (An4+) with a high charge is crucial for understanding their solution chemistry, particularly in nuclear fuel reprocessing and environmental behavior. Using Th4+ as a reference of the An4+ series, this work employed both the periodic model and the cluster model to calculate the first hydrolysis reaction constant (pKa1) of the Th4+ aqua ion and conducted a detailed evaluation of these approaches. In the periodic model, ab initio molecular dynamics (AIMD) simulations of Th4+ in the explicit solvation environment are conducted, using metadynamics and constrained molecular dynamics to calculate pKa1 values. Metadynamics simulations with sufficient sampling yielded a value of 5.02, aligning with the experimental values (4.12-4.97). Moreover, AIMD results reveal further Grotthuss-type proton transfers and changes in the solvent structures, which are important for accurately modeling the hydrolysis process. In the cluster model, density functional theory calculations are performed on isolated hydrate clusters to obtain pKa1 values, describing solvation effects through the cluster-continuum model. Based on insights from the periodic models, particularly regarding further proton transfer, the cluster model was modified and tested using different functionals and similar cations (La3+and Ac3+). The pKa1 values obtained in the cluster model also show good agreement with the experimental values. The current computational approaches provide a comprehensive understanding of Th4+ hydrolysis and a reference framework for studying the hydrolysis of other lanthanide and actinide ions.

Second Hydration Shell of Mg2+: Competition between Ion-Water Interaction and Hydrogen Bonding Interaction

Hydration in Mg2+ solutions is critical in the chemical and biological industries. Researchers have identified a rigid first hydration shell, but the effects of ion-water and hydrogen bonding (HB) interactions beyond the first shell of Mg2+, especially when ion pairs form at high concentrations, remain controversial. On the basis of density functional theory, machine learning molecular dynamics was performed to study the second shell of Mg2+ in MgCl2 solutions at various concentrations. At low concentrations, while both SCAN and PBE+TS-vdW predict a rigid first shell, SCAN affords a more softened structure due to its weakened HB interaction. The weakened HB interaction reveals the retarding effect of Mg2+ on the water reorientation of the second shell. With an increasing concentration, SCAN reproduces the decreasing trend of the hydration number, which originates from Cl- entering the second shell of Mg2+. Our results highlight the importance of accurately described ion-water interaction and HB interaction in the intermediate range.

The Dynamic Diversity and Invariance of Ab Initio Water

Comprehending water dynamics is crucial in various fields, such as water desalination, ion separation, electrocatalysis, and biochemical processes. While ab initio molecular dynamics (AIMD) accurately portray water's structure, computing its dynamic properties over nanosecond time scales proves cost-prohibitive. This study employs machine learning potentials (MLPs) to accurately determine the dynamic properties of liquid water with ab initio accuracy. Our findings reveal diversity in the calculated diffusion coefficient (D) and viscosity of water (η) across different methodologies. Specifically, while the GGA, meta-GGA, and hybrid functional methods struggle to predict dynamic properties under ambient conditions, methods on the higher level of Jacob's ladder of DFT approximation perform significantly better. Intriguingly, we discovered that both D and η adhere to the established Stokes-Einstein (SE) relation for all of the ab initio water. The diversity observed across different methods can be attributed to distinct structural entropy, affirming the applicability of excess entropy scaling relations across all functionals. The correlation between D and η provides valuable insights for identifying the ideal temperature to accurately replicate the dynamic properties of liquid water. Furthermore, our findings can validate the rationale behind employing artificially high temperatures in the simulation of water via AIMD. These outcomes not only pave the path to designing better functionals for water but also underscore the significance of water's many-body characteristics.

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.

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.

Structure and self-diffusivity of mixed-cation electrolytes between neutral and charged graphene sheets

Graphene-based applications, such as supercapacitors or capacitive deionization, take place in an aqueous environment, and they benefit from molecular-level insights into the behavior of aqueous electrolyte solutions in single-digit graphene nanopores with a size comparable to a few molecular diameters. Under single-digit graphene nanoconfinement (smallest dimension <2 nm), water and ions behave drastically different than in the bulk. Most aqueous electrolytes in the graphene-based applications as well as in nature contain a mix of electrolytes. We study several prototypical aqueous mixed alkali-chloride electrolytes containing an equimolar fraction of Li/Na, Li/K, or Na/K cations confined between neutral and positively or negatively charged parallel graphene sheets. The strong hydration shell of small Li+ vs a larger Na+ or large K+ with weaker or weak hydration shells affects the interplay between the ions's propensity to hydrate or dehydrate under the graphene nanoconfinement and the strength of the ion-graphene interactions mediated by confinement-induced layered water. We perform molecular dynamics simulations of the confined mixed-cation electrolytes using the effectively polarizable force field for electrolyte-graphene systems and focused on a relation between the electrochemical adsorption and structural properties of the water molecules and ions and their diffusion behavior. The simulations show that the one-layer nanoslits have the biggest impact on the ions' adsorption and the water and ions' diffusion. The positively charged one-layer nanoslits only allow for Cl- adsorption and strengthen the intermolecular bonding, which along with the ultrathin confinement substantially reduces the water and Cl- diffusion. In contrast, the negatively charged one-layer nanoslits only allow for adsorption of weakly hydrated Na+ or K+ and substantially break up the non-covalent bond network, which leads to the enhancement of the water and Na+ or K+ diffusion up to or even above the bulk diffusion. In wider nanoslits, cations adsorb closer to the graphene surfaces than Cl-'s with preferential adsorption of a weakly hydrated cation over a strongly hydrated cation. The positive graphene charge has an intuitive effect on the adsorption of weakly hydrated Na+'s or K+'s and Cl-'s and a counterintuitive effect on the adsorption of strongly hydrated Li+'s. On the other hand, the negative surface charge has an intuitive effect on the adsorption of both types of cations and only mild intuitive or counterintuitive effects on the Cl- adsorption. The diffusion of water molecules and ions confined in the wider nanoslits is reduced with respect to the bulk diffusion, more for the positive graphene charge, which strengthened the intermolecular bonding, and less for the negative surface charge, which weakened the non-covalent bond network.

Molecular Insights into the Influence of Ions on the Water Structure. I. Alkali Metal Ions in Solution

In this study, we explore the impact of alkali metal ions (Li+, Na+, K+, Rb+, and Cs+) on the hydration structure of water using molecular dynamics simulations carried out with MB-nrg potential energy functions (PEFs). Our analyses include radial distribution functions, coordination numbers, dipole moments, and infrared spectra of water molecules, calculated as a function of solvation shells. The results collectively indicate a highly local influence of all of the alkali metal ions on the hydrogen-bond network established by the surrounding water molecules, with the smallest and most densely charged Li+ ion exerting the most pronounced effect. Remarkably, the MB-nrg PEFs demonstrate excellent agreement with available experimental data for the position and size of the first solvation shells, underscoring their potential as predictive models for realistic simulations of ionic aqueous solutions across various thermodynamic conditions and environments.

The Missing Chalcogen Bonding Donor: Strongly Polarized Oxygen of Water

A biscyclen molecular cabin, synthesized by connecting two cyclen macrocycles with four linkages, entraps a Li+···H2O···Li+ trimer with a water molecule clamped by two Li+ ions. This configuration results in strongly polarized water, characterized by a water proton resonance shift of up to 10.00 ppm. The arrangement facilitates unprecedented O-centered chalcogen bonds between the lone pairs of pyridinyl nitrogen atoms and polarized water oxygen, as confirmed by X-ray crystallography, NMR spectroscopy, and theoretical calculations. Further observation of O-centered chalcogen bonding in a H2O·(LiCl)2 cluster suggests its widespread presence in hydrated salt systems.

Unlocking osmotic energy harvesting potential in challenging real-world hypersaline environments through vermiculite-based hetero-nanochannels

Nanochannel membranes have demonstrated remarkable potential for osmotic energy harvesting; however, their efficiency in practical high-salinity systems is hindered by reduced ion selectivity. Here, we propose a dual-separation transport strategy by constructing a two-dimensional (2D) vermiculite (VMT)-based heterogeneous nanofluidic system via an eco-friendly and scalable method. The cations are initially separated and enriched in micropores of substrates during the transmembrane diffusion, followed by secondary precise sieving in ultra-thin VMT laminates with high ion flux. Resultantly, our nanofluidic system demonstrates efficient osmotic energy harvesting performance, especially in hypersaline environment. Notably, we achieve a maximum power density of 33.76 W m-2, a 6.2-fold improvement with a ten-fold increase in salinity gradient, surpassing state-of-the-art nanochannel membranes under challenging conditions. Additionally, we confirm practical hypersaline osmotic power generation using various natural salt-lake brines, achieving a power density of 25.9 W m-2. This work triggers the hopes for practical blue energy conversion using advanced nanoarchitecture.

Balance between Physical Interpretability and Energetic Predictability in Widely Used Dispersion-Corrected Density Functionals

We assess the performance of different dispersion models for several popular density functionals across a diverse set of noncovalent systems, ranging from the benzene dimer to molecular crystals. By analyzing the interaction energies and their individual components, we demonstrate that there exists variability across different systems for empirical dispersion models, which are calibrated for reproducing the interaction energies of specific systems. Thus, parameter fitting may undermine the underlying physics, as dispersion models rely on error compensation among the different components of the interaction energy. Energy decomposition analyses reveal that, the accuracy of revPBE-D3 for some aqueous systems originates from significant compensation between dispersion and charge transfer energies. However, revPBE-D3 is less accurate in describing systems where error compensation is incomplete, such as the benzene dimer. Such cases highlight the propensity for unpredictable behavior in various dispersion-corrected density functionals across a wide range of molecular systems, akin to the behavior of force fields. On the other hand, we find that SCAN-rVV10, a targeted-dispersion approach, affords significant reductions in errors associated with the lattice energies of molecular crystals, while it has limited accuracy in reproducing structural properties. Given the ubiquitous nature of noncovalent interactions and the key role of density functional theory in computational sciences, the future development of dispersion models should prioritize the faithful description of the dispersion energy, a shift that promises greater accuracy in capturing the underlying physics across diverse molecular and extended systems.

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.

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.

Structure and self-diffusivity of alkali-halide electrolytes in neutral and charged graphene nanochannels

Understanding the microscopic behaviour of aqueous electrolyte solutions in graphene-based ultrathin nanochannels is important in nanofluidic applications such as water purification, fuel cells, and molecular sensing. Under extreme confinement (<2 nm), the properties of water and ions differ drastically from those in the bulk phase. We studied the structural and diffusion behaviour of prototypical aqueous solutions of electrolytes (LiCl, NaCl, and KCl) confined in both neutral and positively-, and negatively-charged graphene nanochannels. We performed molecular dynamics simulations of the solutions in the nanochannels with either one, two- or three-layer water structures using the effectively polarisable force field for graphene. We analysed the structure and intermolecular bond network of the confined solutions along with their relation to the self-diffusivity of water and ions. The simulations show that Na and K cations can more easily rearrange their solvation shells under the graphene nanoconfinement and adsorb on the graphene surfaces or dissolve in the confinement-induced layered water than the Li cation. The negative surface charge together with the presence of ions orient water molecules with hydrogens towards the graphene surfaces, which in turn weakens the intermolecular bond network. The one-layer nanochannels have the biggest effect on the water structure and intermolecular bonding as well as on the adsorption of ions with only co-ions entering these nanochannels. The self-diffusivity of confined water is strongly reduced with respect to the bulk water and decreases with diminishing nanochannel heights except for the negatively-charged one-layer nanochannel. The self-diffusivity of ions also decreases with the reducing the nanochannel heights except for the self-diffusivity of cations in the negatively-charged one-layer nanochannel, evidencing cooperative diffusion of confined water and ions. Due to the significant break-up of the intermolecular bond network in the negatively-charged one-layer nanochannel, self-diffusion coefficients of water and cations exceed those for the two- and three-layer nanochannels and become comparable to the bulk values.

Competition between Hydration Shell and Ordered Water Chain Induces Thickness-Dependent Desalination Performance in Carbon Nanotube Membrane

Exploring new reverse osmosis (RO) membranes that break the permeability-selectivity trade-off rule is the ultimate goal in seawater desalination. Both nanoporous monolayer graphene (NPG) and carbon nanotube (CNT) channels have been proposed to be promising candidates for this purpose. From the perspective of membrane thickness, both NPG and CNT can be classified into the same category, as NPG is equivalent to the thinnest CNT. While NPG has the advantage of a high water flux rate and CNT is excellent at salt rejection performance, a transition is expected in practical devices when the channel thickness increases from NPG to infinite-sized CNTs. By employing molecular dynamics (MD) simulations, we find that as the thickness of CNT increases, the water flux diminishes but the ion rejection rate increases. These transitions lead to optimal desalination performance around the cross-over size. Further molecular analysis reveals that this thickness effect originates from the formation of two hydration shells and their competition with the ordered water chain structure. With the increase in CNT thickness, the competition-dominated ion path through CNT is further narrowed. Once above this cross-over size, the highly confined ion path remains unchanged. Thus, the number of reduced water molecules also tends to stabilize, which explains the saturation of the salt rejection rate with the increasing CNT thickness. Our results offer insights into the molecular mechanisms of the thickness-dependent desalination performance in a one-dimensional nanochannel, which can provide useful guidance for the future design and optimization of new desalination membranes.