Solubility of KF in water by molecular dynamics using the Kirkwood integration method

Polymorph-Specific Solubility Prediction of Urea Using Constant Chemical Potential Molecular Dynamics Simulations

Molecular dynamics simulations offer a robust approach to understanding the material properties within a system. Solubility is defined as the analytical composition of a saturated solution expressed as a proportion of designated solute in a designated solvent, according to IUPAC. It is a critical property of compounds and holds significance across numerous fields. Various computational techniques have been explored for determining solubility, including methods based on chemical potential determination, enhanced sampling simulation, and direct coexistence simulation, and lately, machine learning-based methods have shown promise. In this investigation, we have utilized Constant Chemical Potential Molecular Dynamics, a method rooted in direct coexistence simulation, to predict the solubility of urea polymorphs in aqueous solution. The primary purpose of using this method is to overcome the limitation of the direct simulation method by maintaining a constant chemical potential for a sufficiently long time. Urea is chosen as a prototypical system for our study, with a particular focus on three of its polymorphs. Our approach effectively discriminates between the polymorphs of urea based on their respective solubility values; polymorph III is found to have the highest solubility, followed by forms IV and I.

Alchemical Osmostat for Monte Carlo Simulation: Sampling Aqueous Electrolyte Solution in Open Systems

Molecular simulations involving electrolytes are usually performed at a fixed amount of salt ions in the simulation box, reproducing macroscopic concentration. Although this statement is valid in the bulk, the concentration of an electrolyte confined in nanoporous materials such as MOFs or zeolites is greatly affected and remains a priori unknown. The nanoporous material in equilibrium with the bulk electrolyte exchange water and ions at a given chemical potential Δμ in the semi-grand-canonical ensemble, that must be calibrated in order to determine the concentration in the nanoporous material. In this work, we propose an algorithm based on nonequilibrium candidate Monte Carlo (NCMC) moves to ultimately perform MC simulations in contact with a saline reservoir. First, we adapt the Widom insertion technique to calibrate the chemical potential by alchemically transmuting water molecules into ions by using NCMC moves. The chemical potential defines a Monte Carlo osmostat in the semi-grand-constant volume and temperature ensemble (Δμ, N, V, T) to be added in a Monte Carlo simulation where the number of ions fluctuates. In order to validate the method, we adapted the NCMC move to determine the free energy of water solvation and subsequently explore thermodynamics of electrolyte solvation at infinite dilution in water. Finally, we implemented the osmostat in MC simulations initialized with bulk water that are driven toward electrolyte solutions of similar concentration as the saline reservoir. Our results demonstrate that alchemical osmostat for MC simulation is a promising tool for use to sample electrolyte insertion in nanoporous materials.

Computing the Liquidus of Binary Monatomic Salt Mixtures with Direct Simulation and Alchemical Free Energy Methods

We describe and validate a free-energy-based method for computing the liquidus for binary solid-liquid phase diagrams in molecular simulations of monatomic salts. The method is demonstrated by calculating the liquidus for LiCl-KCl and MgCl₂-KCl salt mixtures with the polarizable ion model (PIM). The free-energy-based method is cross-validated with direct coexistence simulations. Both techniques show excellent agreement with one another. Though the predictions of the PIM disagree with experiments, we use our free-energy-based approach to decouple the contributions of liquid mixture nonidealities and pure component solid-liquid equilibrium to the phase diagram. In both mixtures, the PIM accurately reproduces the liquid phase nonidealities but fails to predict the liquidus because it does not accurately predict the pure component melting temperature of LiCl or MgCl₂.

Molecular Mechanism of Gas Solubility in Liquid: Constant Chemical Potential Molecular Dynamics Simulations

Accurate prediction of gas solubility in a liquid is crucial in many areas of chemistry, and a detailed understanding of the molecular mechanism of the gas solvation continues to be an active area of research. Here, we extend the idea of the constant chemical potential molecular dynamics (CμMD) approach to the calculation of the gas solubility in the liquid under constant gas chemical potential conditions. As a representative example, we utilize this method to calculate the isothermal solubility of carbon dioxide in water. Additionally, we provide microscopic insight into the mechanism of solvation that preferentially occurs in areas of the surface where the hydrogen network is broken.

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.

Challenges in the use of atomistic simulations to predict solubilities of drug-like molecules

Background: Solubility is a physical property of high importance to the pharmaceutical industry, the prediction of which for potential drugs has so far been a hard task. We attempted to predict the solubility of acetylsalicylic acid (ASA) by estimating the absolute chemical potentials of its most stable polymorph and of solutions with different concentrations of the drug molecule. Methods: Chemical potentials were estimated from all-atom molecular dynamics simulations.  We used the Einstein molecule method (EMM) to predict the absolute chemical potential of the solid and solvation free energy calculations to predict the excess chemical potentials of the liquid-phase systems. Results: Reliable estimations of the chemical potentials for the solid and for a single ASA molecule using the EMM required an extremely large number of intermediate states for the free energy calculations, meaning that the calculations were extremely demanding computationally. Despite the computational cost, however, the computed value did not agree well with the experimental value, potentially due to limitations with the underlying energy model. Perhaps better values could be obtained with a better energy model; however, it seems likely computational cost may remain a limiting factor for use of this particular approach to solubility estimation.    Conclusions: Solubility prediction of drug-like solids remains computationally challenging, and it appears that both the underlying energy model and the computational approach applied may need improvement before the approach is suitable for routine use.

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.

Addressing hysteresis and slow equilibration issues in cavity-based calculation of chemical potentials

In this paper, we explore the strengths and weaknesses of a cavity-based method to calculate the excess chemical potential of a large molecular solute in a dense liquid solvent. Use of the cavity alleviates some technical problems associated with the appearance of (integrable) divergences in the integrand during alchemical particle growth. The excess chemical potential calculated using the cavity-based method should be independent of the cavity attributes. However, the performance of the method (equilibration time and the robustness) does depend on the cavity attributes. To illustrate the importance of a suitable choice of the cavity attributes, we calculate the partition coefficient of pyrene in toluene and heptane using a coarse-grained model. We find that a poor choice for the functional form of the cavity may lead to hysteresis between growth and shrinkage of the cavity. Somewhat unexpectedly, we find that, by allowing the cavity to move as a pseudo-particle within the simulation box, the decay time of fluctuations in the integrand of the thermodynamic integration can be reduced by an order of magnitude, thereby increasing the statistical accuracy of the calculation.

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.

Computational prediction of drug solubility in water-based systems: Qualitative and quantitative approaches used in the current drug discovery and development setting

In this review we will discuss recent advances in computational prediction of solubility in water-based solvents. Our focus is set on recent advances in predictions of biorelevant solubility in media mimicking the human intestinal fluids and on new methods to predict the thermodynamic cycle rather than prediction of solubility in pure water through quantitative structure property relationships (QSPR). While the literature is rich in QSPR models for both solubility and melting point, a physicochemical property strongly linked to the solubility, recent advances in the modelling of these properties make use of theory and computational simulations to better predict these properties or processes involved therein (e.g. solid state crystal lattice packing, dissociation of molecules from the lattice and solvation). This review serves to provide an update on these new approaches and how they can be used to more accurately predict solubility, and also importantly, inform us on molecular interactions and processes occurring during drug dissolution and solubilisation.

Solubility prediction from first principles: a density of states approach

Solubility is a fundamental property of widespread significance. Its accurate prediction remains a major challenge. We present a novel, efficient approach to solubility prediction for molecules over a range of conditions based on density of states.

Approaches for calculating solvation free energies and enthalpies demonstrated with an update of the FreeSolv database

Solvation free energies can now be calculated precisely from molecular simulations, providing a valuable test of the energy functions underlying these simulations. Here, we briefly review "alchemical" approaches for calculating the solvation free energies of small, neutral organic molecules from molecular simulations, and illustrate by applying them to calculate aqueous solvation free energies (hydration free energies). These approaches use a non-physical pathway to compute free energy differences from a simulation or set of simulations and appear to be a particularly robust and general-purpose approach for this task. We also present an update (version 0.5) to our FreeSolv database of experimental and calculated hydration free energies of neutral compounds and provide input files in formats for several simulation packages. This revision to FreeSolv provides calculated values generated with a single protocol and software version, rather than the heterogeneous protocols used in the prior version of the database. We also further update the database to provide calculated enthalpies and entropies of hydration and some experimental enthalpies and entropies, as well as electrostatic and nonpolar components of solvation free energies.

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

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

Consensus on the solubility of NaCl in water from computer simulations using the chemical potential route

The solubility of NaCl in water is evaluated by using three force field models: Joung-Cheatham for NaCl dissolved in two different water models (SPC/E and TIP4P/2005) and Smith Dang NaCl model in SPC/E water. The methodology based on free-energy calculations [E. Sanz and C. Vega, J. Chem. Phys. 126, 014507 (2007)] and [J. L. Aragones et al., J. Chem. Phys. 136, 244508 (2012)] has been used, except, that all calculations for the NaCl in solution were obtained by using molecular dynamics simulations with the GROMACS package instead of homemade MC programs. We have explored new lower molalities and made longer runs to improve the accuracy of the calculations. Exploring the low molality region allowed us to obtain an analytical expression for the chemical potential of the ions in solution as a function of molality valid for a wider range of molalities, including the infinite dilute case. These new results are in better agreement with recent estimations of the solubility obtained with other methodologies. Besides, two empirical simple rules have been obtained to have a rough estimate of the solubility of a certain model, by analyzing the ionic pairs formation as a function of molality and/or by calculating the difference between the NaCl solid chemical potential and the standard chemical potential of the salt in solution.

Using MD Simulations To Calculate How Solvents Modulate Solubility

Here, our interest is in predicting solubility in general, and we focus particularly on predicting how the solubility of particular solutes is modulated by the solvent environment. Solubility in general is extremely important, both for theoretical reasons - it provides an important probe of the balance between solute-solute and solute-solvent interactions - and for more practical reasons, such as how to control the solubility of a given solute via modulation of its environment, as in process chemistry and separations. Here, we study how the change of solvent affects the solubility of a given compound. That is, we calculate relative solubilities. We use MD simulations to calculate relative solubility and compare our calculated values with experiment as well as with results from several other methods, SMD and UNIFAC, the latter of which is commonly used in chemical engineering design. We find that straightforward solubility calculations based on molecular simulations using a general small-molecule force field outperform SMD and UNIFAC both in terms of accuracy and coverage of the relevant chemical space.

Mean ionic activity coefficients in aqueous NaCl solutions from molecular dynamics simulations

The mean ionic activity coefficients of aqueous NaCl solutions of varying concentrations at 298.15 K and 1 bar have been obtained from molecular dynamics simulations by gradually turning on the interactions of an ion pair inserted into the solution. Several common non-polarizable water and ion models have been used in the simulations. Gibbs-Duhem equation calculations of the thermodynamic activity of water are used to confirm the thermodynamic consistency of the mean ionic activity coefficients. While the majority of model combinations predict the correct trends in mean ionic activity coefficients, they overestimate their values at high salt concentrations. The solubility predictions also suffer from inaccuracies, with all models underpredicting the experimental values, some by large factors. These results point to the need for further ion and water model development.

The effect of concentration- and temperature-dependent dielectric constant on the activity coefficient of NaCl electrolyte solutions

Our implicit-solvent model for the estimation of the excess chemical potential (or, equivalently, the activity coefficient) of electrolytes is based on using a dielectric constant that depends on the thermodynamic state, namely, the temperature and concentration of the electrolyte, ε(c, T). As a consequence, the excess chemical potential is split into two terms corresponding to ion-ion (II) and ion-water (IW) interactions. The II term is obtained from computer simulation using the Primitive Model of electrolytes, while the IW term is estimated from the Born treatment. In our previous work [J. Vincze, M. Valiskó, and D. Boda, "The nonmonotonic concentration dependence of the mean activity coefficient of electrolytes is a result of a balance between solvation and ion-ion correlations," J. Chem. Phys. 133, 154507 (2010)], we showed that the nonmonotonic concentration dependence of the activity coefficient can be reproduced qualitatively with this II+IW model without using any adjustable parameter. The Pauling radii were used in the calculation of the II term, while experimental solvation free energies were used in the calculation of the IW term. In this work, we analyze the effect of the parameters (dielectric constant, ionic radii, solvation free energy) on the concentration and temperature dependence of the mean activity coefficient of NaCl. We conclude that the II+IW model can explain the experimental behavior using a concentration-dependent dielectric constant and that we do not need the artificial concept of "solvated ionic radius" assumed by earlier studies.

Predicting the excess solubility of acetanilide, acetaminophen, phenacetin, benzocaine, and caffeine in binary water/ethanol mixtures via molecular simulation

We present a general framework to predict the excess solubility of small molecular solids (such as pharmaceutical solids) in binary solvents via molecular simulation free energy calculations at infinite dilution with conventional molecular models. The present study used molecular dynamics with the General AMBER Force Field to predict the excess solubility of acetanilide, acetaminophen, phenacetin, benzocaine, and caffeine in binary water/ethanol solvents. The simulations are able to predict the existence of solubility enhancement and the results are in good agreement with available experimental data. The accuracy of the predictions in addition to the generality of the method suggests that molecular simulations may be a valuable design tool for solvent selection in drug development processes.

A method for computing the solubility limit of solids: application to sodium chloride in water and alcohols

We present an adaptable method to compute the solubility limit of solids by molecular simulation, which avoids the difficulty of reference state calculations. In this way, the method is highly adaptable to molecules of complex topology. Results are shown for solubility calculations of sodium chloride in water and light alcohols at atmospheric conditions. The pseudosupercritical path integration method is used to calculate the free energy of the solid and gives results that are in good agreement with previous studies that reference the Einstein crystal. For the solution phase calculations, the self-adaptive Wang-Landau transition-matrix Monte Carlo method is used within the context of an expanded isothermal-isobaric ensemble. The method shows rapid convergence properties and the uncertainty in the calculated chemical potential was 1% or less for all cases. The present study underpredicts the solubility limit of sodium chloride in water, suggesting a shortcoming of the molecular models. Importantly, the proper trend for the chemical potential in various solvents was captured, suggesting that relative solubilities can be computed by the method.