Recent progress in molecular simulation of aqueous electrolytes: force fields, chemical potentials and solubility

A Method for Efficiently Predicting the Radial Distribution Function and Osmotic Coefficients of Aqueous Electrolyte Solutions

The prediction of the structural and thermodynamic properties of electrolyte solutions is critical for a huge range of practical situations where these solutions play a vital role. Theoretical models, such as the continuum solvent model, attempt to explain the behavior of solutions using a coarse-grained description of the interactions of species in the solution, whereas molecular simulations aim to directly compute the behavior of the solution, including the interactions between all ions and molecules in the system. Both methods have limitations: theoretical models are generally less accurate because they rely on assumptions, while molecular simulations require significant computational resources, particularly if higher accuracy is desired. To address these issues, we propose an affordable and effective method that combines the advantages of the modified Poisson-Boltzmann equation (MPBE) with classical molecular dynamics (MD) simulations to predict the radial distribution functions and thermodynamic properties of electrolyte solutions. We demonstrate a method of using the MPBE to compute the short-range potential of mean force (PMF) from the radial distribution functions (RDFs) and vice versa. Furthermore, we provide insights into the relationship between the RDFs and the short-range PMF based on the MPBE. Our analysis reveals that the effective short-range PMFs can be approximately calculated using low concentration simulations but the short-range PMFs are slightly concentration-dependent in simulations at higher concentrations. Additionally, we demonstrate that for concentrated solutions, osmotic coefficients can be calculated in agreement with experiment using a virial approach. This is based on the effective short-range PMFs and RDFs obtained from the MPBE method. Our proposed MPBE can therefore accelerate the calculation of the structural and thermodynamic properties of electrolyte solutions.

Hygroscopic Growth of Adsorbed Water Films on Smectite Clay Particles

Hygroscopic growth of adsorbed water films on clay particles underlies a number of environmental science questions, from the air quality and climate impacts of mineral dust aerosols to the hydrology and mechanics of unsaturated soils and sedimentary rocks. Here, we use molecular dynamics (MD) simulations to establish the relation between adsorbed water film thickness (h) and relative humidity (RH) or disjoining pressure (Π), which has long been uncertain due to factors including sensitivity to particle shape, surface roughness, and aqueous chemistry. We present a new MD simulation approach that enables precise quantification of Π in films up to six water monolayers thick. We find that the hygroscopicity of phyllosilicate mineral surfaces increases in the order mica < K-smectite < Na-smectite. The relationship between Π and h on clay surfaces follows a double exponential decay with e-folding lengths of 2.3 and 7.5 Å. The two decay length scales are attributed to hydration repulsion and osmotic phenomena in the electrical double layer (EDL) at the clay-water interface.

A streamlined molecular-dynamics workflow for computing solubilities of molecular and ionic crystals

Computing the solubility of crystals in a solvent using atomistic simulations is notoriously challenging due to the complexities and convergence issues associated with free-energy methods, as well as the slow equilibration in direct-coexistence simulations. This paper introduces a molecular-dynamics workflow that simplifies and robustly computes the solubility of molecular or ionic crystals. This method is considerably more straightforward than the state-of-the-art, as we have streamlined and optimised each step of the process. Specifically, we calculate the chemical potential of the crystal using the gas-phase molecule as a reference state, and employ the S0 method to determine the concentration dependence of the chemical potential of the solute. We use this workflow to predict the solubilities of sodium chloride in water, urea polymorphs in water, and paracetamol polymorphs in both water and ethanol. Our findings indicate that the predicted solubility is sensitive to the chosen potential energy surface. Furthermore, we note that the harmonic approximation often fails for both molecular crystals and gas molecules at or above room temperature, and that the assumption of an ideal solution becomes less valid for highly soluble substances.

Transport Properties of NaCl in Aqueous Solution and Hydrogen Solubility in Brine

Ion transport properties and hydrogen solubility in brine play pivotal roles in various engineering and scientific scopes including chemical, physical, geochemical, and geothermal domains. Molecular dynamics simulations were performed to obtain transport properties of NaCl in the binary H2O + NaCl system using different force fields. Brine density, ion diffusivity, molar conductivity, conductivity, and hydrogen solubilities were obtained as functions of temperature and salt concentration. We compared the performance of different force fields against the experimental correlation model and developed three mathematical models. The first was the modified brine density model based on the simulated brine density over a wide range of salinity levels, and the second and third analytical mathematical models were derived for the ion diffusivity and molar conductivity as a function of salinity and temperature. The results of this study illustrated that the modified brine density model not only produced the same results of the previous model for lower salinity levels but also applied well to predict the brine density for a higher salinity level. The derived mathematical models indicated that the ion diffusivity and molar conductivity decreased linearly with salinity, and the slope and y-intercept of the lines of diffusivity and molar conductivity versus temperature were third-order polynomials of temperature. The developed models provided the mechanism for the behavior of decreasing molar conductivity with increasing salinity and increasing conductivity with increasing salinity. The directions of the effect of salinity on the molar conductivity and conductivity were opposite. The molar conductivity increased with a decreasing salinity level. However, the conductivity increased with increasing salinity, as the contribution of the ion concentration or salinity level to conductivity dominated over that of the ion movement.

Self-Consistent Implementation of a Solvation Free Energy Framework to Predict the Salt Solubilities of Six Alkali Halides

To assess the salt solubilities of six alkali halides in aqueous systems, we proposed a thermodynamic cycle and an efficient molecular modeling methodology. The Gibbs free energy changes for vaporization, dissociation, and dissolution were calculated using the experimental data of ionic thermodynamic properties obtained from the NBS tables. Additionally, the Marcus' and Tissandier's solvation free energy data for Li+, Na+, K+, Cl-, and Br- ions were compared with the conventional solvation free energies by substituting into our self-consistent thermodynamic cycle. Furthermore, Tissandier's absolute solvation free energy data were used as the training set to refit the Lennard-Jones parameters of OPLS-AA force field for ions. To predict salt solubilities, an assumption of a pseudo-solvent was proposed to characterize the coupling work of a solute with its environment from infinitely diluted to saturated solutions, indicating that the Gibbs energy change of solvation process is a function of ionic strength. Following the self-consistency of the cycle, the newly derived formulas were used to determine the salt solubilities by interpolating the intersection of Gibbs free energy of dissolution and the zero free energy line. The refined ion parameters can also predict the structure and thermodynamic properties of aqueous electrolyte solutions, such as densities, pair correlation functions, hydration numbers, mean activity coefficients, vapor pressures, and the radial dependences of the net charge at 298.15 K and 1 bar. Our method can be used to characterize the solid-liquid equilibria of ions or charged particles in aqueous systems. Furthermore, for highly concentrated strong electrolyte systems, it is essential to introduce accurate water models and polarizable force fields.

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.

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.

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.

Solubilities and Transport Properties of CO2, Oxalic Acid, and Formic Acid in Mixed Solvents Composed of Deep Eutectic Solvents, Methanol, and Propylene Carbonate

Recently, deep eutectic solvents (DES) have been considered as possible electrolytes for the electrochemical reduction of CO₂ to value-added products such as formic and oxalic acids. The applicability of pure DES as electrolytes is hindered by high viscosities. Mixtures of DES with organic solvents can be a promising way of designing superior electrolytes by exploiting the advantages of each solvent type. In this study, densities, viscosities, diffusivities, and ionic conductivities of mixed solvents comprising DES (i.e., reline and ethaline), methanol, and propylene carbonate were computed using molecular simulations. To provide a quantitative assessment of the affinity and mass transport of CO₂ and oxalic and formic acids in the mixed solvents, the solubilities and self-diffusivities of these solutes were also computed. Our results show that the addition of DES to the organic solvents enhances the solubilities of oxalic and formic acids, while the solubility of CO₂ in the ethaline-containing mixtures are in the same order of magnitude with the respective pure organic components. A monotonic increase in the densities and viscosities of the mixed solvents is observed as the mole fraction of DES in the mixture increases, with the exception of the density of ethaline-propylene carbonate which shows the opposite behavior due to the high viscosity of the pure organic component. The self-diffusivities of all species in the mixtures significantly decrease as the mole fraction of DES approaches unity. Similarly, the self-diffusivities of the dissolved CO₂ and the oxalic and formic acids also decrease by at least 1 order of magnitude as the composition of the mixture shifts from the pure organic component to pure DES. The computed ionic conductivities of all mixed solvents show a maximum value for mole fractions of DES in the range from 0.2 to 0.6 and decrease as more DES is added to the mixtures. Since for most mixtures studied here no prior experimental measurements exist, our findings can serve as a first data set based on which further investigation of DES-containing electrolyte solutions can be performed for the electrochemical reduction of CO₂ to useful chemicals.

Where Lennard-Jones Potentials Fail: Iterative Optimization of Ion-Water Pair Potentials Based on Ab Initio Molecular Dynamics Data

The use of the Lennard-Jones (LJ) potential in computer simulations of aqueous electrolyte solutions is widespread. The standard approach is to parametrize LJ potential parameters against thermodynamic solution properties, but problems in representing the local structural and dynamic properties of ion hydration shells remain. The r^-12-term in the LJ potential is responsible for this as it leads to overly repulsive ion-water interactions at short range. As a result, the LJ potential predicts blue-shifted vibrational peaks of the cations' rattling mode and too large negative ion hydration entropies. We demonstrate that cation-water effective pair potentials derived from ab initio MD data have softer short-range repulsions and represent hydration shell properties significantly better. Our findings indicate that replacing the LJ potential with these effective pair potentials offers a promising route to represent thermodynamic solution properties and local interactions of specific ions with nonpolarizable force field models.

Activity Coefficients and Solubilities of NaCl in Water-Methanol Solutions from Molecular Dynamics Simulations

We obtain activity coefficients and solubilities of NaCl in water-methanol solutions at 298.15 K and 1 bar from molecular dynamics (MD) simulations with the Joung-Cheatham, SPC/E, and OPLS-AA force fields for NaCl, water, and methanol, respectively. The Lorentz-Berthelot combining rules were adopted for the unlike-pair interactions of Na⁺, Cl^-, and the oxygen site in SPC/E water, and geometric combining rules were utilized for the remainder of the cross interactions. We found that the selection of appropriate combining rules is important in obtaining physically realistic solubilities. The solvent compositions studied range from pure water to pure methanol. Several salt concentrations were investigated at each solvent composition, from the lowest concentrations permitted by the system size used up to the experimental solubilities. We first calculated individual ion activity coefficients (IIACs) for Na⁺ and Cl^- from the free energy change due to the gradual insertion of a single cation or anion into the solution, accompanied by a neutralizing background. We obtained the salt solubilities by comparing the chemical potentials in solution with solid NaCl chemical potentials calculated previously using the Einstein crystal method. Mean ionic activity coefficients obtained from the IIACs are in reasonable agreement with experimental data, with deviations increasing for solutions of higher methanol content. Predictions for the salt solubility are in surprisingly good agreement with experimental data, despite well-known challenges in the simultaneous calculation of activity coefficients and solubilities with classical MD simulations. The present study demonstrates that good predictions for these two important phase equilibrium properties can be obtained for mixed-solvent electrolyte solutions using existing nonpolarizable models and further suggests that the previously proposed single ion insertion technique can be extended to complex mixed-solvent solutions as well.

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.

Molecular Simulations of Aqueous Electrolytes: Role of Explicit Inclusion of Charge Transfer into Force Fields

We describe here simulations of aqueous salt solutions that are performed using an explicit charge transfer force field. The emphasis of the discussion is on the calculation of a dynamical property of the solutions: self-diffusion of water. While force fields that are based on pairwise additive potentials or on potentials with explicit inclusion of polarization or with scaled charges can provide at best a qualitative agreement with experiments, force fields with explicit inclusion of charge transfer can produce quantitative agreement with experiment for NaCl and KCl solutions. We argue that a force field with explicit charge transfer contains new physics absent in the previously used force fields described in recent reviews of molecular simulations of aqueous electrolytes.

Activity coefficients of aqueous electrolytes from implicit-water molecular dynamics simulations

We obtain activity coefficients in NaCl and KCl solutions from implicit-water molecular dynamics simulations, at 298.15 K and 1 bar, using two distinct approaches. In the first approach, we consider ions in a continuum with constant relative permittivity (ɛ_r) equal to that of pure water; in the other approach, we take into account the concentration-dependence of ɛ_r, as obtained from explicit-water simulations. Individual ion activity coefficients (IIACs) are calculated using gradual insertion of single ions with uniform neutralizing backgrounds to ensure electroneutrality. Mean ionic activity coefficients (MIACs) obtained from the corresponding IIACs in simulations with constant ɛ_r show reasonable agreement with experimental data for both salts. Surprisingly, large systematic negative deviations are observed for both IIACs and MIACs in simulations with concentration-dependent ɛ_r. Our results suggest that the absence of hydration structure in implicit-water simulations cannot be compensated by correcting for the concentration-dependence of the relative permittivity ɛ_r. Moreover, even in simulations with constant ɛ_r for which the calculated MIACs are reasonable, the relative positioning of IIACs of anions and cations is incorrect for NaCl. We conclude that there are severe inherent limitations associated with implicit-water simulations in providing accurate activities of aqueous electrolytes, a finding with direct relevance to the development of electrolyte theories and to the use and interpretation of implicit-solvent simulations.

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.

Bursting the bubble: A molecular understanding of surfactant-water interfaces

Surfactant science has historically emphasized bulk, thermodynamic measurements to understand the microemulsion properties of greatest industrial significance, such as interfacial tensions, phase behavior, and thermal stability. Recently, interest in the molecular properties of surfactants has grown among the physical chemistry community. This has led to the application of cutting-edge spectroscopic methods and advanced simulations to understand the specific interactions that give rise to the previously studied bulk characteristics. In this Perspective, we catalog key findings that describe the surfactant-oil and surfactant-water interfaces in molecular detail. We emphasize the role of ultrafast spectroscopic methods, including two-dimensional infrared spectroscopy and sum-frequency-generation spectroscopy, in conjunction with molecular dynamics simulations, and the role these techniques have played in advancing our understanding of interfacial properties in surfactant microemulsions.

"In Silico" Seawater

Many important processes affecting the earth's climate are determined by the physical properties of seawater. In addition, desalination of seawater is a significant source of drinking water for the human population living in coastal areas. Since the physical properties of seawater governing these processes depend on the molecular interactions among its components, a deeper knowledge of seawater at the molecular level would contribute to a better understanding of these phenomena. However, in strong contrast with the situation in other areas such as biomolecules or materials science, molecular simulation studies reporting the physical properties of seawater are currently lacking. This is probably due to the usual perception of the seawater composition being too complex to approach. This point of view ignores the fact that physical properties of seawater are dependent on a single parameter representing the composition, namely the salinity. This is because the relative proportions of any two major constituents of seasalt are always the same. Another obstacle to performing molecular simulations of seawater could have been the unavailability of a satisfactory force field representing the interactions between water molecules and dissolved substances. However, this drawback has recently been overcome with the proposal of the Madrid-2019 force field. In this work we show for the first time that molecular simulation of seawater is feasible. We have performed molecular dynamics simulations of a system, the composition of which is close to the average composition of standard seawater and with the molecular interactions given by the Madrid-2019 force field. In this way we are able to provide quantitative or semiquantitative predictions for a number of relevant physical properties of seawater for temperatures and salinities from the oceanographic range to those relevant to desalination processes. The computed magnitudes include static (density), dynamical (viscosity and diffusion coefficients), structural (ionic hydration, ion-ion distribution functions), and interfacial (surface tension) properties.

Molecular modeling of aqueous electrolytes at interfaces: Effects of long-range dispersion forces and of ionic charge rescaling

Molecular dynamics simulations of aqueous electrolytes generally rely on empirical force fields, combining dispersion interactions-described by a truncated Lennard-Jones (LJ) potential-and electrostatic interactions-described by a Coulomb potential computed with a long-range solver. Recently, force fields using rescaled ionic charges [electronic continuum correction (ECC)], possibly complemented with rescaling of LJ parameters [ECC rescaled (ECCR)], have shown promising results in bulk, but their performance at interfaces has been less explored. Here, we started by exploring the impact of the LJ potential truncation on the surface tension of a sodium chloride aqueous solution. We show a discrepancy between the numerical predictions for truncated LJ interactions with a large cutoff and for untruncated LJ interactions computed with a long-range solver, which can bias comparison of force field predictions with experiments. Using a long-range solver for LJ interactions, we then show that an ionic charge rescaling factor chosen to correct long-range electrostatic interactions in bulk accurately describes image charge repulsion at the liquid-vapor interface, and the rescaling of LJ parameters in ECCR models-aimed at capturing local ion-ion and ion-water interactions in bulk- describes well the formation of an ionic double layer at the liquid-vapor interface. Overall, these results suggest that the molecular modeling of aqueous electrolytes at interfaces would benefit from using long-range solvers for dispersion forces and from using ECCR models, where the charge rescaling factor should be chosen to correct long-range electrostatic interactions.

Role of Viscosity in Deviations from the Nernst-Einstein Relation

Deviations from the Nernst-Einstein relation are commonly attributed to ion-ion correlation and ion pairing. Despite the fact that these deviations can be quantified by either experimental measurements or molecular dynamics simulations, there is no rule of thumb to tell the extent of deviations. Here, we show that deviations from the Nernst-Einstein relation are proportional to the inverse viscosity by exploring the finite-size effect on transport properties under periodic boundary conditions. This conclusion is in accord with the established experimental results of ionic liquids.

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.

Hybrid Solvation Model with First Solvation Shell for Calculation of Solvation Free Energy

We present a hybrid solvation model with first solvation shell to calculate solvation free energies. This hybrid model combines the quantum mechanics and molecular mechanics methods with the analytical expression based on the Born solvation model to calculate solvation free energies. Based on calculated free energies of solvation and reaction profiles in gas phase, we set up a unified scheme to predict reaction profiles in solution. The predicted solvation free energies and reaction barriers are compared with experimental results for twenty bimolecular nucleophilic substitution reactions. These comparisons show that our hybrid solvation model can predict reliable solvation free energies and reaction barriers for chemical reactions of small molecules in aqueous solution.

Dielectric Decrement for Aqueous NaCl Solutions: Effect of Ionic Charge Scaling in Nonpolarizable Water Force Fields

We investigate the dielectric constant and the dielectric decrement of aqueous NaCl solutions by means of molecular dynamic simulations. We thereby compare the performance of four different force fields and focus on disentangling the origin of the dielectric decrement and the influence of scaled ionic charges, as often used in nonpolarizable force fields to account for the missing dynamic polarizability in the shielding of electrostatic ion interactions. Three of the force fields showed excessive contact ion pair formation, which correlates with a reduced dielectric decrement. In spite of the fact that the scaling of charges only weakly influenced the average polarization of water molecules around an ion, the rescaling of ionic charges did influence the dielectric decrement, and a close-to-linear relation of the slope of the dielectric constant as a function of concentration with the ionic charge was found.

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.

Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li+ Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations

A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy Δ_s G_M⁺,wat^◦ of the Li⁺ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy [Formula: see text] of the proton, the surface electric potential jump χ_wat^◦ upon entering bulk water, and the absolute single-electrode potential [Formula: see text] of the reference hydrogen electrode are calculated to be -1099.9 ± 4.2 kJ·mol^-1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (-1100 ± 5 kJ·mol^-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li⁺ are also compared to those for Na⁺ and K⁺ from a previous study in terms of relative hydration free energies ΔΔ_s G_M⁺,wat^◦ and relative electrode potentials [Formula: see text]. The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔ_s G_M⁺,wat^• and redox potentials [Formula: see text]. The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller-Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li⁺ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.

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.