A Kirkwood-Buff Derived Force Field for Aqueous Alkali Halides

Effect of K+ Force Fields on Ionic Conductivity and Charge Dynamics of KOH in Ethylene Glycol

Predicting ionic conductivity is crucial for developing efficient electrolytes for energy storage and conversion and other electrochemical applications. An accurate estimate of ionic conductivity requires understanding complex ion-ion and ion-solvent interactions governing the charge transport at the molecular level. Molecular simulations can provide key insights into the spatial and temporal behavior of electrolyte constituents. However, such insights depend on the ability of force fields to describe the underlying phenomena. In this work, molecular dynamics simulations were leveraged to delineate the impact of force field parameters on ionic conductivity predictions of potassium hydroxide (KOH) in ethylene glycol (EG). Four different force fields were used to represent the K+ ion. Diffusion-based Nernst-Einstein and correlation-based Einstein approaches were implemented to estimate the ionic conductivity, and the predicted values were compared with experimental measurements. The physical aspects, including ion-aggregation, charge distribution, cluster correlation, and cluster dynamics, were also examined. A force field was identified that provides reasonably accurate Einstein conductivity values and a physically coherent representation of the electrolyte at the molecular level.

Unveiling the Borohydride Ion through Force-Field Development

The borohydride ion, BH4-, is an essential reducing agent in many technological processes, yet its full understanding has been elusive, because of at least two significant challenges. One challenge arises from its marginal stability in aqueous solutions outside of basic pH conditions, which considerably limits the experimental thermodynamic data. The other challenge comes from its unique and atypical hydration shell, stemming from the negative excess charge on its hydrogen atoms, which complicates the accurate modeling in classical atomistic simulations. In this study, we combine experimental and computer simulation techniques to devise a classical force field for NaBH4 and deepen our understanding of its characteristics. We report the first measurement of the ion's activity coefficient and extrapolate it to neutral pH conditions. Given the difficulties in directly measuring its solvation free energies, owing to its instability, we resort to quantum chemistry calculations. This combined strategy allows us to derive a set of nonpolarizable force-field parameters for the borohydride ion for classical molecular dynamics simulations. The derived force field simultaneously captures the solvation free energy, the hydration structure, as well as the activity coefficient of NaBH4 salt across a broad concentration range. The obtained insights into the hydration shell of the BH4- ion are crucial for accurately modeling and understanding its interactions with other molecules, ions, materials, and interfaces.

Madrid-2019 force field: An extension to divalent cations Sr2+ and Ba2

In this work, we present a parameterization of Sr2+ and Ba2+ cations, which expands the alkali earth set of cations of the Madrid-2019 force field. We have tested the model against the experimental densities of eight different salts, namely, SrCl2, SrBr2, SrI2, Sr(NO3)2, BaCl2, BaBr2, BaI2, and Ba(NO3)2. The force field is able to reproduce the experimental densities of all these salts up to their solubility limit. Furthermore, we have computed the viscosities for two selected salts, finding that the experimental values are overestimated, but the predictions are still reasonable. Finally, the structural properties for all the salts have been calculated with this model and align remarkably well with experimental observations.

Lipid shape and packing are key for optimal design of pH-sensitive mRNA lipid nanoparticles

The ionizable-lipid component of RNA-containing nanoparticles controls the pH-dependent behavior necessary for an efficient delivery of the cargo-the so-called endosomal escape. However, it is still an empirical exercise to identify optimally performing lipids. Here, we study two well-known ionizable lipids, DLin-MC3-DMA and DLin-DMA using a combination of experiments, multiscale computer simulations, and electrostatic theory. All-atom molecular dynamics simulations, and experimentally measured polar headgroup pKa values, are used to develop a coarse-grained representation of the lipids, which enables the investigation of the pH-dependent behavior of lipid nanoparticles (LNPs) through Monte Carlo simulations, in the absence and presence of RNA molecules. Our results show that the charge state of the lipids is determined by the interplay between lipid shape and headgroup chemistry, providing an explanation for the similar pH-dependent ionization state observed for lipids with headgroup pKa values about one-pH-unit apart. The pH dependence of lipid ionization is significantly influenced by the presence of RNA, whereby charge neutrality is achieved by imparting a finite and constant charge per lipid at intermediate pH values. The simulation results are experimentally supported by measurements of α-carbon 13C-NMR chemical shifts for eGFP mRNA LNPs of both DLin-MC3-DMA and DLin-DMA at various pH conditions. Further, we evaluate the applicability of a mean-field Poisson-Boltzmann theory to capture these phenomena.

Scaling Solute-Solvent Distances to Improve Solubility and Ion Paring Predictions in Rigid Ion Models

Force fields based on the rigid ion model (RIM) have been developed to accurately predict the various physical and chemical properties of salts and water. However, the combined use of these models often fails to accurately predict the solubility of salts in water. To address this issue, several approaches, such as charge scaling or reparameterization, have been proposed. Nevertheless, these methods require laborious reparameterization of nonbonded force field parameters. In this article, we propose a scaling solute-solvent distance (SSSD) method to improve force fields in predicting salt solubility without changing the solute-solute and solvent-solvent interactions in the original force fields. This method can also tune the ion pairing of salt in water. One main advantage of the SSSD method is that reparameterization of the crystal and water models is not needed. We use two RIMs for the NaCl-water system (JC-SPC/E and SD-SPC/E) and the CHARMM force field for the KCl-water system to demonstrate the improved accuracy in predicting solubility by the SSSD method. Furthermore, we use the RDG-SPC/Fw force field to show that the SSSD method can also be used to tune the ion pairing of CaCO3 in water. Limitations of this method are also discussed.

A Nanoconfined Water-Ion Coordination Network for Flexible Energy-Dissipation Devices

Water-ion interaction in a nanoconfined environment that deeply constrains spatial freedoms of local atomistic motion with unconventional coupling mechanisms beyond that in a free, bulk state is essential to spark designs of a broad spectrum of nanofluidic devices with unique properties and functionalities. Here, it is reported that the interaction between ions and water molecules in a hydrophobic nanopore forms a coordination network with an interaction density that is nearly fourfold that of the bulk counterpart. Such strong interaction facilitates the connectivity of the water-ion network and is uncovered by corroborating the formation of ion clusters and the reduction of particle dynamics. A liquid-nanopore energy-dissipation system is designed and demonstrated in both molecular simulations and experiments that the formed coordination network controls the outflow of confined electrolytes along with a pressure reduction, capable of providing flexible protection for personnel and devices and instrumentations against external mechanical impact and attack.

Computation of Electrical Conductivities of Aqueous Electrolyte Solutions: Two Surfaces, One Property

In this work, we computed electrical conductivities under ambient conditions of aqueous NaCl and KCl solutions by using the Einstein-Helfand equation. Common force fields (charge q = ±1 e) do not reproduce the experimental values of electrical conductivities, viscosities, and diffusion coefficients. Recently, we proposed the idea of using different charges to describe the potential energy surface (PES) and the dipole moment surface (DMS). In this work, we implement this concept. The equilibrium trajectories required to evaluate electrical conductivities (within linear response theory) were obtained by using scaled charges (with the value q = ±0.75 e) to describe the PES. The potential parameters were those of the Madrid-Transport force field, which accurately describe viscosities and diffusion coefficients of these ionic solutions. However, integer charges were used to compute the conductivities (thus describing the DMS). The basic idea is that although the scaled charge describes the ion-water interaction better, the integer charge reflects the value of the charge that is transported due to the electric field. The agreement obtained with experiments is excellent, as for the first time electrical conductivities (and the other transport properties) of NaCl and KCl electrolyte solutions are described with high accuracy for the whole concentration range up to their solubility limit. Finally, we propose an easy way to obtain a rough estimate of the actual electrical conductivity of the potential model under consideration using the approximate Nernst-Einstein equation, which neglects correlations between different ions.

Scaled charges for ions: An improvement but not the final word for modeling electrolytes in water

In this work, we discuss the use of scaled charges when developing force fields for NaCl in water. We shall develop force fields for Na⁺ and Cl^- using the following values for the scaled charge (in electron units): ±0.75, ±0.80, ±0.85, and ±0.92 along with the TIP4P/2005 model of water (for which previous force fields were proposed for q = ±0.85 and q = ±1). The properties considered in this work are densities, structural properties, transport properties, surface tension, freezing point depression, and maximum in density. All the developed models were able to describe quite well the experimental values of the densities. Structural properties were well described by models with charges equal to or larger than ±0.85, surface tension by the charge ±0.92, maximum in density by the charge ±0.85, and transport properties by the charge ±0.75. The use of a scaled charge of ±0.75 is able to reproduce with high accuracy the viscosities and diffusion coefficients of NaCl solutions for the first time. We have also considered the case of KCl in water, and the results obtained were fully consistent with those of NaCl. There is no value of the scaled charge able to reproduce all the properties considered in this work. Although certainly scaled charges are not the final word in the development of force fields for electrolytes in water, its use may have some practical advantages. Certain values of the scaled charge could be the best option when the interest is to describe certain experimental properties.

Simulating Polyproline II-Helix-Rich Peptides with the Latest Kirkwood-Buff Force Field: A Direct Comparison with AMBER and CHARMM

We simulated the dynamics of a set of peptides characterized by ensembles rich in PPII-helical content, to assess the ability of the most recent Kirkwood-Buff force field (KBFF20) to sample this conformational peculiarity. KBFF has been previously shown to capably reproduce experimental dimensions of disordered proteins, while being limited in confidently sampling structured proteins. Further development of the force field bridged this gap. It is however still unknown what are the main differences between KBFF and AMBER/CHARMM force fields. A direct comparison is now possible as both AMBER/CHARMM force fields have been used to sample peptides rich in PPII-helical content. We found that KBFF20 samples' PPII-helical content qualitatively matches both AMBER and CHARMM force fields, with the main difference being the KBFF ability to populate the α_R region of the Ramachandran plot in the set of simulated peptides. Overall, KBFF20 is a well-balanced force field, able to sample the dynamics of both structured and unstructured proteins.

Shining (Infrared) Light on the Hofmeister Series: Driving Forces for Changes in the Water Vibrational Spectra in Alkali-Halide Salt Solutions

The Hofmeister series is frequently used to rank ions based on their behavior from chaotropes ("structure breakers"), which weaken the surrounding hydrogen-bond network, to kosmotropes ("structure makers"), which enhance it. Here, we use fluctuation theory to investigate the energetic and entropic driving forces underlying the Hofmeister series for aqueous alkali-halide solutions. Specifically, we exploit the OH stretch infrared (IR) spectrum in isotopically dilute HOD/D₂O solutions as a probe of the effect of the salt on the water properties for different concentrations and choice of halide anion. Fluctuation theory is used to calculate the temperature derivative of these IR spectra, including decomposition of the derivative into different energetic contributions. These contributions are used to determine the thermodynamic driving forces in terms of effective internal energy and entropic contributions. This analysis implicates entropic contributions as the key factor in the Hofmeister series behavior of the OH stretch IR spectra, while the effective internal energy is nearly ion-independent.

Impacts of targeting different hydration free energy references on the development of ion potentials

Hydration free energy (HFE) as the most important solvation parameter is often targeted in ion model development, even though the reported values differ by dozens of kcal mol^-1 mainly due to the experimentally undetermined HFE of the proton ΔG°(H⁺). The choice of ΔG°(H⁺) obviously affects the hydration of single ions and the relative HFE between the ions with different (magnitude or sign) charges, and the impacts of targeted HFEs on the ion solvation and ion-ion interactions are largely unrevealed. Here we designed point charge models of K⁺, Mg²⁺, Al³⁺, and Cl^- ions targeting a variety of HFE references and then investigated the HFE influences on the simulations of dilute and concentrated ion solutions and of the salt ion pairs in gas, liquid, and solid phases. Targeting one more property of ion-water oxygen distances (IOD) leaves the ion-water binding distance invariant, while the binding strength increases with the decreasing (more negative) HFE of ions as a result of a decrease in ΔG°(H⁺) for the cation and an increase in ΔG°(H⁺) for the anion. The increase in ΔG°(H⁺) leads to strengthened cation-anion interactions and thus to close ion-ion contacts, low osmotic pressures, and small activity derivatives in concentrated ion solutions as well as too stable ion pairs of the salts in different phases. The ion diffusivity and water exchange rates around the ions are simply not HFE dependent but rather more complex. Targeting both the aqueous IOD and salt crystal properties of KCl was also attempted and the comparison between different models indicates the complexity and challenge in obtaining a balanced performance between different phases using classical force fields. Our results also support that a real ΔG°(H⁺) value of -259.8 kcal mol^-1 recommended by Hünenberger and Reif guides ion models to reproduce ion-water and ion-ion interactions reasonably at relatively low salt concentrations. Simulations of a metalloprotein show that a relatively more positive ΔG°(H⁺) for Mg²⁺ model is better for a reasonable description of the metal binding network.

Influence of ion specificity and concentration on the conformational transition of intrinsically disordered sheep prion peptide

The structural sensitivity of the IDPs with the ions has been observed experimentally; however, it is still unclear how the presence of different metal ions affects structural stability. We performed atomistic molecular dynamics simulation of sheep prion peptide (142-167) in presence of different monovalent, divalent ions at various concentrations to find out the effect of the size, charge, and ionic concentration on the structure of the peptide. It is found that Li + ions have a higher survival probability compared to Na + , K + and Mg2 + affecting the solvation structure of the protein leading to the alpha-helix structure. At high concentration, due to the increase in the ion-solvent and ion-counter interactions, the effect of the ions is screened on the surface of the protein and hence no ion specificity is observed. This study demonstrates how ions can be used to regulate the protein structure and function that can help in designing drugs.

Magnesium Force Fields for OPC Water with Accurate Solvation, Ion-Binding, and Water-Exchange Properties: Successful Transfer from SPC/E

Magnesium plays a vital role in a large variety of biological processes. To model such processes by molecular dynamics simulations, researchers rely on accurate force field parameters for Mg2+ and water. OPC is one of the most promising water models yielding an improved description of biomolecules in water. The aim of this work is to provide force field parameters for Mg2+ that lead to accurate simulation results in combination with OPC water. Using twelve different Mg2+ parameter sets, that were previously optimized with different water models, we systematically assess the transferability to OPC based on a large variety of experimental properties. The results show that the Mg2+ parameters for SPC/E are transferable to OPC and closely reproduce the experimental solvation free energy, radius of the first hydration shell, coordination number, activity derivative, and binding affinity toward the phosphate oxygens on RNA. Two optimal parameter sets are presented: MicroMg yields water exchange in OPC on the microsecond timescale in agreement with experiments. NanoMg yields accelerated exchange on the nanosecond timescale and facilitates the direct observation of ion binding events for enhanced sampling purposes.

Optimized Magnesium Force Field Parameters for Biomolecular Simulations with Accurate Solvation, Ion-Binding, and Water-Exchange Properties in SPC/E, TIP3P-fb, TIP4P/2005, TIP4P-Ew, and TIP4P-D

Magnesium is essential in many vital processes. To correctly describe Mg2+ in physiological processes by molecular dynamics simulations, accurate force fields are fundamental. Despite the importance, force fields based on the commonly used 12-6 Lennard-Jones potential showed significant shortcomings. Recently progress was made by an optimization procedure that implicitly accounts for polarizability. The resulting microMg and nanoMg force fields (J. Chem. Theory Comput. 2021, 17, 2530-2540) accurately reproduce a broad range of experimental solution properties and the binding affinity to nucleic acids in TIP3P water. Since countless simulation studies rely on available water models and ion force fields, we here extend the optimization and provide Mg2+ parameters in combination with the SPC/E, TIP3P-fb, TIP4P/2005, TIP4P-Ew, and TIP4P-D water models. For each water model, the Mg2+ force fields reproduce the solvation free energy, the distance to oxygens in the first hydration shell, the hydration number, the activity coefficient derivative in MgCl2 solutions, and the binding affinity and distance to the phosphate oxygens on nucleic acids. We present two parameter sets: MicroMg yields water exchange on the microsecond time scale and matches the experimental exchange rate. Depending on the water model, nanoMg yields accelerated water exchange in the range of 106 to 108 exchanges per second. The nanoMg parameters can be used to enhance the sampling of binding events, to obtain converged distributions of Mg2+, or to predict ion binding sites in biomolecular simulations. The parameter files are freely available at https://github.com/bio-phys/optimizedMgFFs.

Measurement of Enthalpies and Entropies of Activation as a Function of Pairwise Distance for the Pairwise Relative Diffusion of SrI2 in Water over Lengthscales from 6 Å to 40 Å

Quasi-elastic neutron scattering (QENS) has been used to provide insight into the motions within solutions for many decades, and coherent QENS (CQENS) determines the motions of one ion relative to...

Contribution of Different Molecules and Moieties to the Surface Tension in Aqueous Surfactant Solutions. II: Role of the Size and Charge Sign of the Counterions

Understanding the role of the counterion species in surfactant solutions is a complicated task, made harder by the fact that, experimentally, it is not possible to vary independently bulk and surface quantities. Here, we perform molecular dynamics simulations at constant surface coverage of the liquid/vapor interface of lithium, sodium, potassium, rubidium, and cesium dodecyl sulfate aqueous solutions. We investigate the effect of counterion type and charge sign on the surface tension of the solution, analyzing the contribution of different species and moieties to the lateral pressure profile. The observed trends are qualitatively compatible with the Hofmeister series, with the notable exception of sodium. We point out a possible shortcoming of what is at the moment, in our experience, the most realistic nonpolarizable force field (CHARMM36) that includes the parametrization for the whole series of alkali counterions. In the artificial system where the counterion and surfactant charges are inverted in sign, the counterions become considerably harder. This charge inversion changes considerably the surface tension contributions of the counterions, surfactant headgroups, and water molecules, stressing the key role of the hardness of the counterions in this respect. However, the hydration free energy gain of the counterions, occurring upon charge inversion, is compensated by the concomitant free energy loss of the headgroups and water molecules, leading to a negligible change in the surface tension of the entire system.

Individual Ion Activity Coefficients in Aqueous Electrolytes from Explicit-Water Molecular Dynamics Simulations

We compute individual ion activity coefficients (IIACs) in aqueous NaCl, KCl, NaF, and KF solutions from explicit-water molecular dynamics simulations. Free energy changes are obtained from insertion of single ions-accompanied by uniform neutralizing backgrounds-into solution by gradually turning on first Lennard-Jones interactions, followed by Coulombic interactions using Ewald electrostatics. Simulations are performed at multiple system sizes, and all results are extrapolated to the thermodynamic limit, thus eliminating any possible artifacts from the neutralizing backgrounds. Because of controversies associated with measurements of IIACs from electrochemical cells with ion-selective electrodes, the reported experimental data are not widely accepted; thus there remains a knowledge gap with respect to the contributions of individual ions to solution nonidealities. Our results are in good qualitative agreement with these reported measurements, though significantly larger in magnitude. In particular, the relative positioning for the activity coefficients of anions and cations matches the experimental ordering for all four systems. This work establishes a robust thermodynamic framework, without a need to invoke extra hypotheses, that sheds light on the behavior of individual ions and their contributions to nonidealities of aqueous electrolyte solutions.

Proteins maintain hydration at high [KCl] concentration regardless of content in acidic amino acids

Proteins of halophilic organisms, which accumulate molar concentrations of KCl in their cytoplasm, have a much higher content in acidic amino acids than proteins of mesophilic organisms. It has been proposed that this excess is necessary to maintain proteins hydrated in an environment with low water activity, either via direct interactions between water and the carboxylate groups of acidic amino acids or via cooperative interactions between acidic amino acids and hydrated cations. Our simulation study of five halophilic proteins and five mesophilic counterparts does not support either possibility. The simulations use the AMBER ff14SB force field with newly optimized Lennard-Jones parameters for the interactions between carboxylate groups and potassium ions. We find that proteins with a larger fraction of acidic amino acids indeed have higher hydration levels, as measured by the concentration of water in their hydration shell and the number of water/protein hydrogen bonds. However, the hydration level of each protein is identical at low (b_KCl = 0.15 mol/kg) and high (b_KCl = 2 mol/kg) KCl concentrations; excess acidic amino acids are clearly not necessary to maintain proteins hydrated at high salt concentration. It has also been proposed that cooperative interactions between acidic amino acids in halophilic proteins and hydrated cations stabilize the folded protein structure and would lead to slower dynamics of the solvation shell. We find that the translational dynamics of the solvation shell is barely distinguishable between halophilic and mesophilic proteins; if such a cooperative effect exists, it does not have that entropic signature.

Fick Diffusion Coefficient in Binary Mixtures of [HMIM][NTf2] and Carbon Dioxide by Dynamic Light Scattering and Molecular Dynamics Simulations

Dynamic light scattering (DLS) experiments and equilibrium molecular dynamics (EMD) simulations were performed in the saturated liquid phase of the binary mixture of 1-hexyl-3-methylimidazolium bis(trifluormethylsulfonyl)imide ([HMIM][NTf₂]) and carbon dioxide (CO₂) to access the Fick diffusion coefficient (D₁₁). The investigations were performed within or close to saturation conditions at temperatures between (298.15 and 348.15) K and CO₂ mole fractions (x_CO2) up to 0.81. The DLS experiments were combined with polarization-difference Raman spectroscopy (PDRS) to simultaneously access the composition of the liquid phase. For the first time in an electrolyte-based system, D₁₁ was directly calculated from EMD simulations by accessing the Maxwell-Stefan (MS) diffusion coefficient and the thermodynamic factor. Agreement within combined uncertainties was found between D₁₁ from DLS and EMD simulations for CO₂ mole fractions up to 0.5. In general, an increasing D₁₁ with increasing x_CO2 could be observed, with a local maximum present at a CO₂ mole fraction of about 0.75. The local maximum could be explained by an increasing MS diffusion coefficient with increasing x_CO2 over the entire studied composition range and a decreasing thermodynamic factor at x_CO2 above 0.7. Finally, PDRS and EMD simulations were combined to investigate the influence of the fluid structure on the diffusive process.

Extended magnesium and calcium force field parameters for accurate ion-nucleic acid interactions in biomolecular simulations

Magnesium and calcium play an essential role in the folding and function of nucleic acids. To correctly describe their interactions with DNA and RNA in biomolecular simulations, an accurate parameterization is crucial. In most cases, the ion parameters are optimized based on a set of experimental solution properties such as solvation free energies, radial distribution functions, water exchange rates, and activity coefficient derivatives. However, the transferability of such bulk-optimized ion parameters to quantitatively describe biomolecular systems is limited. Here, we extend the applicability of our previous bulk-optimized parameters by including experimental binding affinities toward the phosphate oxygen on nucleic acids. In particular, we systematically adjust the combination rules that are an integral part of the pairwise interaction potentials of classical force fields. This allows us to quantitatively describe specific ion binding to nucleic acids without changing the solution properties in the most simple and efficient way. We show the advancement of the optimized Lorentz combination rule for two representative nucleic acid systems. For double-stranded DNA, the optimized combination rule for Ca²⁺ significantly improves the agreement with experiments, while the standard combination rule leads to unrealistically distorted DNA structures. For the add A-riboswitch, the optimized combination rule for Mg²⁺ improves the structure of two specifically bound Mg²⁺ ions as judged by the experimental distance to the binding site. Including experimental binding affinities toward specific ion binding sites on biomolecules, therefore, provides a promising perspective to develop a more accurate description of metal cations for biomolecular simulations.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Philosophy and Development of KBFF20

A new classical nonpolarizable force field, KBFF20, for the simulation of peptides and proteins is presented. The force field relies heavily on the use of Kirkwood-Buff theory to provide a comparison of simulated and experimental Kirkwood-Buff integrals for solutes containing the functional groups common in proteins, thus ensuring intermolecular interactions that provide a good balance between the peptide-peptide, peptide-solvent, and solvent-solvent distributions observed in solution mixtures. In this way, it differs significantly from other biomolecular force fields. Further development and testing of the intermolecular potentials are presented here. Subsequently, rotational potentials for the ϕ/ψ and χ dihedral degrees of freedom are obtained by analysis of the Protein Data Bank, followed by small modifications to provide a reasonable balance between simulated and observed α and β percentages for small peptides. This, the first of two articles, describes in detail the philosophy and development behind KBFF20.

Optimized Magnesium Force Field Parameters for Biomolecular Simulations with Accurate Solvation, Ion-Binding, and Water-Exchange Properties

Magnesium ions play an essential role in many vital processes. To correctly describe their interactions in molecular dynamics simulations, an accurate parametrization is crucial. Despite the importance and considerable scientific effort, current force fields based on the commonly used 12-6 Lennard-Jones interaction potential fail to reproduce a variety of experimental solution properties. In particular, no parametrization exists so far that simultaneously reproduces the solvation free energy and the distance to the water oxygens in the first hydration shell. Moreover, current Mg2+ force fields significantly underestimate the rate of water exchange leading to unrealistically slow exchange kinetics. In order to make progress in the development of improved models, we systematically optimize the Mg2+ parameters in combination with the TIP3P water model in a much larger parameter space than previously done. The results show that a long-ranged interaction potential and modified Lorentz-Berthelot combination rules allow us to accurately reproduce multiple experimental properties including the solvation free energy, the distances to the oxygens of the first hydration shell, the hydration number, the activity coefficient derivative in MgCl2 solutions, the self-diffusion coefficient, and the binding affinity to the phosphate oxygen of RNA. Matching this broad range of thermodynamic properties, we present two sets of optimal parameters: MicroMg yields water exchange on the microsecond timescale in agreement with experiments. NanoMg yields water exchange on the nanosecond timescale facilitating the direct observation of ion-binding events. As shown for the example of the add A-riboswitch, the optimized parameters correctly reproduce the structure of specifically bound ions and permit the de novo prediction of Mg2+-binding sites in biomolecular simulations.

A practical guide to biologically relevant molecular simulations with charge scaling for electronic polarization

Molecular simulations can elucidate atomistic-level mechanisms of key biological processes, which are often hardly accessible to experiment. However, the results of the simulations can only be as trustworthy as the underlying simulation model. In many of these processes, interactions between charged moieties play a critical role. Current empirical force fields tend to overestimate such interactions, often in a dramatic way, when polyvalent ions are involved. The source of this shortcoming is the missing electronic polarization in these models. Given the importance of such biomolecular systems, there is great interest in fixing this deficiency in a computationally inexpensive way without employing explicitly polarizable force fields. Here, we review the electronic continuum correction approach, which accounts for electronic polarization in a mean-field way, focusing on its charge scaling variant. We show that by pragmatically scaling only the charged molecular groups, we qualitatively improve the charge-charge interactions without extra computational costs and benefit from decades of force field development on biomolecular force fields.

Surface Affinity of Alkali and Halide Ions in Their Aqueous Solution: Insight from Intrinsic Density Analysis

The surface tension of all aqueous alkali halide solutions is higher than that of pure water. According to the Gibbs adsorption equation, this indicates a net depletion of these ions in the interfacial region. However, simulations and experiments show that large, soft ions, such as I^-, can accumulate at the liquid/vapor interface. The presence of a loose hydration shell is usually considered to be the reason for this behavior. In this work, we perform computer simulations to characterize the liquid-vapor interface of aqueous alkali chloride and sodium halide solutions systematically, considering all ions from Li⁺ to Cs⁺ and from F^- to I^-. Using computational methods for the removal of surface fluctuations, we analyze the structure of the interface at a dramatically enhanced resolution, showing that the positive excess originates in the very first molecular layer and that the next 3-4 layers account for the net negative excess. With the help of a fictitious system with charge-inverted ion pairs, we also show that it is not possible to rationalize the surface affinity of ions in solutions in terms of the properties of anions and cations separately. Moreover, the surface excess is generally dominated by the smaller of the two ions.

Ion and water transport reasonably involves rotation and pseudorotation: measurement and modeling the temperature dependence of small-angle neutron scattering from aqueous SrI2

X-ray and neutron scattering have provided insight into the short range (<8 Å) structures of ionic solutions for over a century. For longer distances, single scattering bands have, however, been seen. For the non-hydrolyzing salt SrI2 in aqueous (D2O) solution, a structure sufficient to scatter slow neutrons has been seen to persist down to a concentration of 0.1 mol L-1 where the measured average spacing between scatterers is over 20 Å. Theoretical studies of such long distance solution structures are difficult, and these difficulties are discussed. The width of the distribution in distances between the scatterers (ions, ion pairs, etc.) remains less than 10 Å, which approximates the average size of the ions and their first hydration shell. Here, we measure the temperature dependence from 10 °C to 90 °C of the small angle neutron scattering (SANS) by a 0.5 molar SrI2 solution in D2O and find that this surprisingly narrow distribution of the distances remains constant within experimental uncertainty. This structure of the ions in the solution appears to endure because changes in interion distances along any single spatial dimension require displacements near the size of a water molecule. Together, the experimental measurements support a rotatory mechanism for simultaneous ion transport and water countertransport. Since rotation minimizes displacement of the solution framework, it is suggested that water transport alone also involves rotation of multimolecular structures, and that the interpretation of single-molecule water rotation is confounded by pseudorotation that results from paired picosecond proton exchanges. It is pointed out that NMR-determined millisecond to microsecond proton exchange times of chelated-metal-ion bound waters and the much faster chelate rotational correlation times around 10 picoseconds, both of which require making and breaking of hydrogen bonds, are difficult to impossible to reconcile.

Generalized Moment Correction for Long-Ranged Electrostatics

Describing long-ranged electrostatics using short-ranged pair potentials is appealing because the computational complexity scales linearly with the number of particles. The foundation of the approach presented here is to mimic the long-ranged medium response by cancelling electric multipoles within a small cutoff sphere. We propose a rigorous and formally exact new method that cancels up to infinitely many multipole moments and is free of operational damping parameters often required in existing theories. Using molecular dynamics simulations of water with and without added salt, we discuss radial distribution functions, Kirkwood–Buff integrals, dielectrics, diffusion coefficients, and angular correlations in relation to existing electrostatic models. We find that the proposed method is an efficient and accurate alternative for handling long-ranged electrostatics as compared to Ewald summation schemes. The methodology and proposed parameterization are applicable also for dipole–dipole interactions.

Dielectric constant and density of aqueous alkali halide solutions by molecular dynamics: A force field assessment

The concentration dependence of the dielectric constant and the density of 11 aqueous alkali halide solutions (LiCl, NaCl, KCl, RbCl, CsCl, LiI, NaI, KI, CsI, KF, and CsF) is investigated by molecular simulation. Predictions using eight non-polarizable ion force fields combined with the TIP4P/ε water model are compared to experimental data. The influence of the water model and the temperature on the results for the NaCl brine are also addressed. The TIP4P/ε water model improves the accuracy of dielectric constant predictions compared to the SPC/E water model. The solution density is predicted well by most ion models. Almost all ion force fields qualitatively capture the decline of the dielectric constant with the increase of concentration for all solutions and with the increase of temperature for NaCl brine. However, the sampled dielectric constant is mostly in poor quantitative agreement with experimental data. These results are related to the microscopic solution structure, ion pairing, and ultimately the force field parameters. Ion force fields with excessive contact ion pairing and precipitation below the experimental solubility limit generally yield higher dielectric constant values. An adequate reproduction of the experimental solubility limit should therefore be a prerequisite for further investigations of the dielectric constant of aqueous electrolyte solutions by molecular simulation.

Role of the Counterions in the Surface Tension of Aqueous Surfactant Solutions. A Computer Simulation Study of Alkali Dodecyl Sulfate Systems

We have investigated the surface tension contributions of the counterions, surfactant headgroups and tails, and water molecules in aqueous alkali dodecyl sulfate (DS) solutions close to the saturated surface concentration by analyzing the lateral pressure profile contribution of these components using molecular dynamics simulations. For this purpose, we have used the combination of two popular force fields, namely KBFF for the counterions and GROMOS96 for the surfactant, which are both parameterized for the SPC/E water model. Except for the system containing Na+ counterions, the surface tension of the surfactant solutions has turned out to be larger rather than smaller than that of neat water, showing a severe shortcoming of the combination of the two force fields. We have traced back this failure of the potential model combination to the unphysically strong attraction of the KBFF counterions, except for Na+, to the anionic head of the surfactants. Despite this failure of the model, we have observed a clear relation between the soft/hard character (in the sense of the Hofmeister series) and the surface tension contribution of the counterions, which, given the above limitations of the model, can only be regarded as an indicative result. We emphasize that the obtained results, although in a twisted way, clearly stress the crucial role the counterions of ionic surfactants play in determining the surface tension of the aqueous surfactant solutions.

Lennard-Jones Parameters Determined to Reproduce the Solubility of NaCl and KCl in SPC/E, TIP3P, and TIP4P/2005 Water

Most classical nonpolarizable ion potential models underestimate the solubility values of NaCl and KCl in water significantly. We determine Lennard-Jones parameters of Na⁺, K⁺, and Cl^- that reproduce the solubility as well as the hydration free energy in dilute aqueous solutions for three water potential models, SPC/E, TIP3P, and TIP4P/2005. The ion-oxygen distance in the solution and the cation-anion distance in salt are also considered in the parametrization. In addition to the target properties, the hydration enthalpy, hydration entropy, self-diffusion coefficient, coordination number, lattice energy, enthalpy of solution, density, viscosity, and number of contact ion pairs are calculated for comparison with 17 frequently used or recently developed ion potential models. The overall performance of each ion model is represented by a global score using a scheme that was originally developed for comparison of water potential models. The global score is better for our models than for the other 17 models not only because of the quite good prediction for the solubility but also because of the relatively small deviation from the experimental value for many of the other properties.

Thermodynamics of N-Isopropylacrylamide in Water: Insight from Experiments, Simulations, and Kirkwood-Buff Analysis Teamwork

The behavior of thermoresponsive polymer poly(N-isopropylacrylamide) (PNiPAM), an essential building block in the design of smart soft materials, in aqueous solutions has attracted much interest, which contrasts with our knowledge of N-isopropylacrylamide (NiPAM) monomer. Strikingly, the physicochemical properties of aqueous NiPAM are similarly rich, and their understanding is far from being complete. This stems from the lack of accurate thermodynamic data and quantitative model for atomistic simulations. In this joint study, we have probed the thermodynamic behavior of aqueous NiPAM by experimental methods, molecular dynamics (MD) simulations, and Kirkwood-Buff (KB) analysis at ambient conditions. From the partial molar volumes and simultaneously correlated osmotic coefficients, with excess partial molar enthalpies of NiPAM in water, the concentration and temperature dependence of KB integrals was determined. For the purpose of this work, we have developed and employed a novel NiPAM force field, which not only reproduces KB integrals (G_ij) and adequately captures macroscopic thermodynamic quantities but also provides more accurate structural insight than the original force fields. We revealed in the vicinity of NiPAM the competing effect of amide hydration with interaction between nonpolar regions. This microscopic picture is reflected in the experimentally observed NiPAM-NiPAM association, which is present from highly dilute conditions up to the solubility limit and is evidenced by G₂₂. From intermediate concentrations, it is accompanied by the existence of apparent dense-water regions, as indicated by positive G₁₁ values. The here-employed KB-based framework provided a mutually consistent thermodynamic and microscopic insight into the NiPAM solution and may be further extended for ion-specific effects. Moreover, our findings contribute to the understanding of thermodynamic grounds behind PNiPAM collapse transition.

A force field of Li+, Na+, K+, Mg2+, Ca2+, Cl-, and SO4 2- in aqueous solution based on the TIP4P/2005 water model and scaled charges for the ions

In this work, a force field for several ions in water is proposed. In particular, we consider the cations Li⁺, Na⁺, K⁺, Mg²⁺, and Ca²⁺ and the anions Cl^- and SO₄ ^2-. These ions were selected as they appear in the composition of seawater, and they are also found in biological systems. The force field proposed (denoted as Madrid-2019) is nonpolarizable, and both water molecules and sulfate anions are rigid. For water, we use the TIP4P/2005 model. The main idea behind this work is to further explore the possibility of using scaled charges for describing ionic solutions. Monovalent and divalent ions are modeled using charges of 0.85 and 1.7, respectively (in electron units). The model allows a very accurate description of the densities of the solutions up to high concentrations. It also gives good predictions of viscosities up to 3 m concentrations. Calculated structural properties are also in reasonable agreement with the experiment. We have checked that no crystallization occurred in the simulations at concentrations similar to the solubility limit. A test for ternary mixtures shows that the force field provides excellent performance at an affordable computer cost. In summary, the use of scaled charges, which could be regarded as an effective and simple way of accounting for polarization (at least to a certain extend), improves the overall description of ionic systems in water. However, for purely ionic systems, scaled charges will not adequately describe neither the solid nor the melt.

Thermodynamic Analysis of n-Hexane-Ethanol Binary Mixtures Using the Kirkwood-Buff Theory

A complete thermodynamic analysis of mixtures consisting of molecules with complex chemical constitution can be rather demanding. The Kirkwood-Buff theory of solutions allows the estimation of thermodynamic properties, which cannot be directly extracted from atomistic simulations, such as the Gibbs energy of mixing (Δ_mix G). In this work, we perform molecular dynamics simulations of n-hexane-ethanol binary mixtures in the liquid state under two temperature-pressure conditions and at various mole fractions. On the basis of the recently published methodology of Galata [ Fluid Phase Equilib. 2018 , 470 , 25 - 37 ] , we first calculate the Kirkwood-Buff integrals in the isothermal-isobaric ( NpT) ensemble, identifying how system size affects their estimation. We then extract the activity coefficients, excess Gibbs energy, excess enthalpy, and excess entropy for the n-hexane-ethanol binary mixtures we simulate. We employ two approaches for quantifying composition fluctuations: one based on counting molecular centers of mass and a second one based on counting molecular segments. Results from the two approaches are practically indistinguishable. We compare our results against predictions of vapor-liquid equilibria obtained in a previous simulation work using the same force field, as well as with experimental data, and find very good agreement. In addition, we develop a simple methodology to identify the hydrogen bonds between ethanol molecules and analyze their effects on mixing properties.

Adsorption of Molecular Nitrogen in Electrical Double Layers near Planar and Atomically Sharp Electrodes

The adsorption of gas molecules at electrode-electrolyte interfaces is an important step in electrochemical reactions. Using molecular dynamics simulations, we investigate the adsorption of dissolved N₂ in the electrical double layers (EDLs) of an aqueous electrolyte near planar and 1 nm radius spherical carbon electrodes. The adsorption of N₂ is found to be overall enriched near neutral electrodes regardless of their surface curvature, although it can be locally enriched or depleted depending on the distance from the electrode surface. In comparison, the adsorption of N₂ in the EDL near negatively charged electrodes is found to increase under a moderate surface charge density, but decrease under a high surface charge density, especially near a planar electrode. By analyzing the potential of mean force for dissolved N₂, the solvent-induced effects are found to play important roles in influencing the adsorption of N₂ in the EDLs. The adsorption behavior of N₂ molecules, especially their dependence on the surface charge and curvature of electrodes, is further rationalized by examining the structure of interfacial water molecules, their interference with the hydration shell of N₂, and their modification by the electrification of electrodes.

Properties of Ion Complexes and Their Impact on Charge Transport in Organic Solvent-Based Electrolyte Solutions for Lithium Batteries: Insights from a Theoretical Perspective

Electrolyte formulations in standard lithium ion and lithium metal batteries are complex mixtures of various components. In this article, we review molecular key principles of ion complexes in multicomponent electrolyte solutions in regards of their influence on charge transport mechanisms. We outline basic concepts for the description of ion–solvent and ion–ion interactions, which can be used to rationalize recent experimental and numerical findings concerning modern electrolyte formulations. Furthermore, we discuss benefits and drawbacks of empirical concepts in comparison to molecular theories of solution for a more refined understanding of ion behavior in organic solvents. The outcomes of our discussion provide a rational for beneficial properties of ions, solvent, co-solvent and additive molecules, and highlight possible routes for further improvement of novel electrolyte solutions.

A polarizable MARTINI model for monovalent ions in aqueous solution

We present a new polarizable coarse-grained martini force field for monovalent ions, called refIon, which is developed mainly for the accurate reproduction of electrostatic properties in aqueous electrolyte solutions. The ion model relies on full long-range Coulomb interactions and introduces satellite charges around the central interaction site in order to model molecular polarization effects. All force field parameters are matched to reproduce the mass density and the static dielectric permittivity of aqueous NaCl solutions, such that experimental values are well-reproduced up to moderate salt concentrations of 2   m o l / l . In addition, an improved agreement with experimentally measured ionic conductivities is observed. Our model is validated with regard to analytic solutions for the ion distribution around highly charged rod-like polyelectrolytes in combination with atomistic simulations and experimental results concerning structural properties of lipid bilayers in the presence of distinct salt concentrations. Further results regarding the coordination numbers of counterions around dilute poly(styrene sulfonate) and poly(diallyldimethylammonium) polyelectrolyte chains also highlight the applicability of our approach. The introduction of our force field allows us to eliminate heuristic scaling factors, as reported for previous martini ion models in terms of effective salt concentrations, and in consequence provides a better agreement between simulation and experimental results. The presented approach is specifically useful for recent martini attempts that focus on highly charged systems-such as models of DNA, polyelectrolytes or polyelectrolyte complexes-where precise studies of electrostatic effects and charge transport processes are essential.

Salt Bridge in Aqueous Solution: Strong Structural Motifs but Weak Enthalpic Effect

Salt bridges are elementary motifs of protein secondary and tertiary structure and are commonly associated with structural driving force that increases stability. Often found on the interface to the solvent, they are highly susceptible to solvent–solute interactions, primarily with water but also with other cosolvents (especially ions). We have investigated the interplay of an Arginine–Aspartic acid salt bridge with simple salt ions in aqueous solution by means of molecular dynamics simulations. Besides structural and dynamical features at equilibrium, we have computed the mean force along the dissociation pathway of the salt bridge. We demonstrate that solvated ions influence the behavior of the salt bridge in a very specific and local way, namely the formation of tight ionic pairs Li⁺/Na⁺–Asp⁻. Moreover, our findings show that the enthalpic relevance of the salt bridge is minor, regardless of the presence of solvated ions.