Solubility of NaCl in water and its melting point by molecular dynamics in the slab geometry and a new BK3-compatible force field

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.

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.

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.

Direct Calculation of the Interfacial Free Energy between NaCl Crystal and Its Aqueous Solution at the Solubility Limit

Salty water is the most abundant electrolyte aqueous mixture on Earth, however, very little is known about the NaCl-saturated solution interfacial free energy (γ_{s}). Here, we provide the first direct estimation of γ_{s} for several NaCl crystallographic planes by means of the mold integration technique, a highly efficient computational method to evaluate interfacial free energies with anisotropic crystal resolution. Making use of the JC-SPC/E model, one of the most benchmarked force fields for NaCl water solutions, we measure γ_{s} of four different crystal planes, (100), (110), (111), and (112[over ¯]) with the saturated solution at normal conditions. We find high anisotropy between the different crystal orientations with values ranging from 100 to 150  mJ m^{-2}, and the average value of the distinct planes being γ[over ¯]_{s}=137(20)  mJ m^{-2}. This value for the coexistence interfacial free energy is in reasonable agreement with previous extrapolations from nucleation studies. Our Letter represents a milestone in the computational calculation of interfacial free energies between ionic crystals and aqueous solutions.

Blinded Predictions and Post Hoc Analysis of the Second Solubility Challenge Data: Exploring Training Data and Feature Set Selection for Machine and Deep Learning Models

Accurate methods to predict solubility from molecular structure are highly sought after in the chemical sciences. To assess the state of the art, the American Chemical Society organized a "Second Solubility Challenge" in 2019, in which competitors were invited to submit blinded predictions of the solubilities of 132 drug-like molecules. In the first part of this article, we describe the development of two models that were submitted to the Blind Challenge in 2019 but which have not previously been reported. These models were based on computationally inexpensive molecular descriptors and traditional machine learning algorithms and were trained on a relatively small data set of 300 molecules. In the second part of the article, to test the hypothesis that predictions would improve with more advanced algorithms and higher volumes of training data, we compare these original predictions with those made after the deadline using deep learning models trained on larger solubility data sets consisting of 2999 and 5697 molecules. The results show that there are several algorithms that are able to obtain near state-of-the-art performance on the solubility challenge data sets, with the best model, a graph convolutional neural network, resulting in an RMSE of 0.86 log units. Critical analysis of the models reveals systematic differences between the performance of models using certain feature sets and training data sets. The results suggest that careful selection of high quality training data from relevant regions of chemical space is critical for prediction accuracy but that other methodological issues remain problematic for machine learning solubility models, such as the difficulty in modeling complex chemical spaces from sparse training data sets.

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.

Dynamics of Aqueous Electrolyte Solutions: Challenges for Simulations

This Perspective article focuses on recent simulation work on the dynamics of aqueous electrolytes. It is well-established that full-charge, nonpolarizable models for water and ions generally predict solution dynamics that are too slow in comparison to experiments. Models with reduced (scaled) charges do better for solution diffusivities and viscosities but encounter issues describing other dynamic phenomena such as nucleation rates of crystals from solution. Polarizable models show promise, especially when appropriately parametrized, but may still miss important physical effects such as charge transfer. First-principles calculations are starting to emerge for these properties that are in principle able to capture polarization, charge transfer, and chemical transformations in solution. While direct ab initio simulations are still too slow for simulations of large systems over long time scales, machine-learning models trained on appropriate first-principles data show significant promise for accurate and transferable modeling of electrolyte solution dynamics.

Obtaining Consistent Free Energies for Ion Binding at Surfaces from Solution: Pathways versus Alchemy for Determining Kink Site Stability

Ion incorporation or removal from a solid at the interface with solution is a fundamental part of crystal growth. Despite this, there have been few quantitative determinations of the thermodynamics for such processes from atomistic molecular dynamics due to the associated technical challenges. In this study, we compute the free energies for ion removal from kink sites at the interface between NaCl and water as an illustrative example. To examine the influence of the free energy technique used, we compare methods that follow an explicit pathway for dissolution with those that focus on the thermodynamics of the initial and final states using metadynamics and free energy perturbation, respectively. While the initial results of the two approaches are found to be completely different, it is demonstrated that the thermodynamics can be reconciled with appropriate corrections for the standard states, thus illustrating the need for caution in interpreting raw free energy curves for ion binding as widely found in the literature. In addition, a new efficient approach is introduced to correct for the system size dependence of kink site energies both due to the periodic interaction of charges in an inhomogeneous dielectric system and due to the dipolar interactions between pairs of kinks along a row. Ultimately, it is shown that with suitable care, both classes of free energy techniques are capable of producing kink site stabilities that are consistent with the solubility of the underlying bulk solid. However, the precise values for individual kink sites exhibit a small systematic offset, which can be ascribed to the contribution of the interfacial potential to the pathway-based results. For the case of NaCl, the free energies of the kink sites relative to a 1 M aqueous solution for Na⁺ and Cl^- are found to be surprisingly different and of opposite sign, despite the ions having very similar hydration free energies.

Freezing point depression of salt aqueous solutions using the Madrid-2019 model

Salt aqueous solutions are relevant in many fields, ranging from biological systems to seawater. Thus, the availability of a force-field that is able to reproduce the thermodynamic and dynamic behavior of salt aqueous solutions would be of great interest. Unfortunately, this has been proven challenging, and most of the existing force-fields fail to reproduce much of their behavior. In particular, the diffusion of water or the salt solubility are often not well reproduced by most of the existing force-fields. Recently, the Madrid-2019 model was proposed, and it was shown that this force-field, which uses the TIP4P/2005 model for water and non-integer charges for the ions, provides a good description of a large number of properties, including the solution densities, viscosities, and the diffusion of water. In this work, we assess the performance of this force-field on the evaluation of the freezing point depression. Although the freezing point depression is a colligative property that at low salt concentrations depends solely on properties of pure water, a good model for the electrolytes is needed to accurately predict the freezing point depression at moderate and high salt concentrations. The coexistence line between ice and several salt aqueous solutions (NaCl, KCl, LiCl, MgCl₂, and Li₂SO₄) up to the eutectic point is estimated from direct coexistence molecular dynamics simulations. Our results show that this force-field reproduces fairly well the experimentally measured freezing point depression with respect to pure water freezing for all the salts and at all the compositions considered.

Homogeneous nucleation of NaCl in supersaturated solutions

The seeding method is an approximate approach to investigate nucleation that combines molecular dynamics simulations with classical nucleation theory. Recently, this technique has been successfully implemented in a broad range of nucleation studies. However, its accuracy is subject to the arbitrary choice of the order parameter threshold used to distinguish liquid-like from solid-like molecules. We revisit here the crystallization of NaCl from a supersaturated brine solution and show that consistency between seeding and rigorous methods, like Forward Flux Sampling (from previous work) or spontaneous crystallization (from this work), is achieved by following a mislabelling criterion to select such threshold (i.e. equaling the fraction of the mislabelled particles in the bulk parent and nucleating phases). This work supports the use of seeding to obtain fast and reasonably accurate nucleation rate estimates and the mislabelling criterion as one giving the relevant cluster size for classical nucleation theory in crystallization studies.

Toward Physics-Based Solubility Computation for Pharmaceuticals to Rival Informatics

We demonstrate that physics-based calculations of intrinsic aqueous solubility can rival cheminformatics-based machine learning predictions. A proof-of-concept was developed for a physics-based approach via a sublimation thermodynamic cycle, building upon previous work that relied upon several thermodynamic approximations, notably the 2RT approximation, and limited conformational sampling. Here, we apply improvements to our sublimation free-energy model with the use of crystal phonon mode calculations to capture the contributions of the vibrational modes of the crystal. Including these improvements with lattice energies computed using the model-potential-based Ψ_mol method leads to accurate estimates of sublimation free energy. Combining these with hydration free energies obtained from either molecular dynamics free-energy perturbation simulations or density functional theory calculations, solubilities comparable to both experiment and informatics predictions are obtained. The application to coronene, succinic acid, and the pharmaceutical desloratadine shows how the methods must be adapted for the adoption of different conformations in different phases. The approach has the flexibility to extend to applications that cannot be covered by informatics methods.

Assessment of hot-melt coating methods for multiparticulate substrates: Mortar-coating vs. pan-coating

Hot-melt coating (HMC) is an alternative, solvent-free coating method generally used to modify substrate release rate and/or mask its unpleasant taste. The aim of this study was to assess two HMC methods (pan-coating and mortar-coating) by assaying functional properties of the coated material. The selected substrates included highly soluble sodium chloride (model substance) and caffeine (bitter drug), and the coating agent was glycerol distearate without/with the addition of liquid paraffin. Experiments with sodium chloride revealed that pan-coating yielded particles of more regular shape, while mortar-coating yielded samples of more uniform coating layer. The flowability of the coated material depended on the particle size. Sustained sodium chloride release was achieved for all mortar-coated and some pan-coated samples. The analysis of the results indicated mortar-coating as a preferable HMC method for caffeine coating. The resulting caffeine yield in the coated samples was high (99%), the material showed satisfactory mechanical properties and drug release from the coated particles was sustained. Overall, the obtained results suggest that both pan-and mortar-coating can be used to sustain the release of drugs with unpleasant taste, but mortar-coating can be considered as a more simple and practical method that can be potentially used in compounding pharmacies.

Absolute chemical potentials for complex molecules in fluid phases: A centroid reference for predicting phase equilibria

Solid-fluid phase equilibria are difficult to predict in simulations because bound degrees of freedom in the crystal phase must be converted to free translations and rotations in the fluid phase. Here, we avoid the solid-to-fluid transformation step by starting with chemical potentials for two reference systems, one for the fluid phase and one for the solid phase. For the solid, we start from the Einstein crystal and transform to the fully interacting molecular crystal. For the fluid phase, we introduce a new reference system, the "centroid," and then transform to gas phase molecules. We illustrate the new calculations by predicting the sublimation vapor pressure of succinic acid in the temperature range of 300 K-350 K.

Pressure in Molecular Simulations with Scaled Charges. 1. Ionic Systems

Charge scaling, rationalized as MDEC (molecular dynamics in electronic continuum) or ECC (electronic continuum correction), has become a widely used simple approach to how to avoid self-consistent induced dipoles yet approximately take into account the effects of electronic polarizability. It has been assumed that the continuum permittivity does not depend on density; in turn, pressure is calculated by standard formulas. In this work, we elaborate a complementary approximation of density-independent molecular polarizability and derive formulas for pressure corrections within the MDEC framework; real behavior lies between these two extremes. The pressure corrections for test ionic systems are huge and negative, leading to sizable densities in constant-pressure MDEC simulations. A comparison of MDEC results with equivalent polarizable systems gives a good pressure match for a crystal but very low MDEC pressures for ionic liquids. These results witness about the importance of a correct density dependence not only of continuum permittivity in MDEC simulations but also of polarizability in polarizable simulations.

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.

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.

Solubility of paracetamol in ethanol by molecular dynamics using the extended Einstein crystal method and experiments

Li and co-workers [Li et al., J. Chem. Phys. 146, 214110 (2017)] have recently proposed a methodology to compute the solubility of molecular compounds from first principles, using molecular dynamics simulations. We revise and further explore their methodology that was originally applied to naphthalene in water at low concentration. In particular, we compute the solubility of paracetamol in an ethanol solution at ambient conditions. For the simulations, we used a force field that we previously reparameterized to reproduce certain thermodynamic properties of paracetamol but not explicitly its solubility in ethanol. In addition, we have determined the experimental solubility by performing turbidity measurements using a Crystal16 over a range of temperatures. Our work serves a dual purpose: (i) methodologically, we clarify how to compute, with a relatively straightforward procedure, the solubility of molecular compounds and (ii) applying this procedure, we show that the solubility predicted by our force field (0.085 ± 0.014 in mole ratio) is in good agreement with the experimental value obtained from our experiments and those reported in the literature (average 0.0585 ± 0.004), considering typical deviations for predictions from first principle methods. The good agreement between the experimental and the calculated solubility also suggests that the method used to reparameterize the force field can be used as a general strategy to optimize force fields for simulations in solution.

Calculation of the water-octanol partition coefficient of cholesterol for SPC, TIP3P, and TIP4P water

We present a numerical study of the relative solubility of cholesterol in octanol and water. Our calculations allow us to compare the accuracy of the computed values of the excess chemical potential of cholesterol for several widely used water models (SPC, TIP3P, and TIP4P). We compute the excess solvation free energies by means of a cavity-based method [L. Li et al., J. Chem. Phys. 146(21), 214110 (2017)] which allows for the calculation of the excess chemical potential of a large molecule in a dense solvent phase. For the calculation of the relative solubility ("partition coefficient," log₁₀ P o / w ) of cholesterol between octanol and water, we use the OPLS/AA force field in combination with the SPC, TIP3P, and TIP4P water models. For all water models studied, our results reproduce the experimental observation that cholesterol is less soluble in water than in octanol. While the experimental value for the partition coefficient is log₁₀ P o / w = 3.7, SPC, TIP3P, and TIP4P give us a value of log₁₀ P o / w = 4.5, 4.6, and 2.9, respectively. Therefore, although the results for the studied water models in combination with the OPLS/AA force field are acceptable, further work to improve the accuracy of current force fields is needed.

Computational methodology for solubility prediction: Application to sparingly soluble organic/inorganic materials

The solubility of a crystalline material can be estimated from the absolute free energy of the solid and the excess solvation free energy. In the earlier work, we presented a general-purpose molecular-dynamics-based methodology enabling solubility predictions of crystalline compounds, yielding accurate estimates of the aqueous solubilities of naphthalene at various pressures and temperatures. In the present work, we investigate a number of prototypical complex materials, including phenanthrene, calcite, and aragonite over a range of temperatures and pressures. Our results provide stronger evidence for the power of the methodology for universal solubility predictions.

Computational methodology for solubility prediction: Application to the sparingly soluble solutes

The solubility of a crystalline substance in the solution can be estimated from its absolute solid free energy and excess solvation free energy. Here, we present a numerical method, which enables convenient solubility estimation of general molecular crystals at arbitrary thermodynamic conditions where solid and solution can coexist. The methodology is based on standard alchemical free energy methods, such as thermodynamic integration and free energy perturbation, and consists of two parts: (1) systematic extension of the Einstein crystal method to calculate the absolute solid free energies of molecular crystals at arbitrary temperatures and pressures and (2) a flexible cavity method that can yield accurate estimates of the excess solvation free energies. As an illustration, via classical Molecular Dynamic simulations, we show that our approach can predict the solubility of OPLS-AA-based (Optimized Potentials for Liquid Simulations All Atomic) naphthalene in SPC (Simple Point Charge) water in good agreement with experimental data at various temperatures and pressures. Because the procedure is simple and general and only makes use of readily available open-source software, the methodology should provide a powerful tool for universal solubility prediction.

Ion dissolution mechanism and kinetics at kink sites on NaCl surfaces

Desolvation barriers are present for solute-solvent exchange events, such as ligand binding to an enzyme active site, during protein folding, and at battery electrodes. For solution-grown crystals, desolvation at kink sites can be the rate-limiting step for growth. However, desolvation and the associated kinetic barriers are poorly understood. In this work, we use rare-event simulation techniques to investigate attachment/detachment events at kink sites of a NaCl crystal in water. We elucidate the desolvation mechanism and present an optimized reaction coordinate, which involves one solute collective variable and one solvent collective variable. The attachment/detachment pathways for Na⁺ and Cl^- are qualitatively similar, with quantitative differences that we attribute to different ion sizes and solvent coordination. The attachment barriers primarily result from kink site desolvation, while detachment barriers largely result from breaking ion-crystal bonds. We compute ion detachment rates from kink sites and compare with results from an independent study. We anticipate that the reaction coordinate and desolvation mechanism identified in this work may be applicable to other alkali halides.