Filip Moučka

Molecular Simulation of Aqueous Electrolyte Solubility. 2. Osmotic Ensemble Monte Carlo Methodology for Free Energy and Solubility Calculations and Application to NaCl

We present a new and computationally efficient methodology using osmotic ensemble Monte Carlo (OEMC) simulation to calculate chemical potential-concentration curves and the solubility of aqueous electrolytes. The method avoids calculations for the solid phase, incorporating readily available data from thermochemical tables that are based on well-defined reference states. It performs simulations of the aqueous solution at a fixed number of water molecules, pressure, temperature, and specified overall electrolyte chemical potential. Insertion/deletion of ions to/from the system is implemented using fractional ions, which are coupled to the system via a coupling parameter λ that varies between 0 (no interaction between the fractional ions and the other particles in the system) and 1 (full interaction between the fractional ions and the other particles of the system). Transitions between λ-states are accepted with a probability following from the osmotic ensemble partition function. Biasing weights associated with the λ-states are used in order to efficiently realize transitions between them; these are determined by means of the Wang-Landau method. We also propose a novel scaling procedure for λ, which can be used for both nonpolarizable and polarizable models of aqueous electrolyte systems. The approach is readily extended to involve other solvents, multiple electrolytes, and species complexation reactions. The method is illustrated for NaCl, using SPC/E water and several force field models for NaCl from the literature, and the results are compared with experiment at ambient conditions. Good agreement is obtained for the chemical potential-concentration curve and the solubility prediction is reasonable. Future improvements to the predictions will require improved force field models.

Molecular force fields for aqueous electrolytes: SPC/E-compatible charged LJ sphere models and their limitations

Thirteen of the most common aqueous NaCl solution force fields based on the SPC/E water solvent are examined with respect to their prediction at ambient conditions of the concentration dependence of the total electrolyte chemical potential and the solution density. We also calculate the salt solubility and the chemical potential and density of the NaCl crystalline solid. We obtain the solution chemical potential in a computationally efficient manner using our recently developed Osmotic Ensemble Monte Carlo method [F. Moučka, M. Lísal, and W. R. Smith, J. Phys. Chem. B 116, 5468 (2012)]. We find that the results of the force fields considered are scattered over a wide range of values, and none is capable of producing quantitatively accurate results over the entire concentration range, with only two of them deemed to be acceptable. Our results indicate that several force fields exhibit precipitation at concentrations below the experimental solubility limit, thus limiting their usefulness. This has important implications, both in general and for their use in biomolecular simulations carried out in the presence of counter-ions. We conclude that either different parameter fitting techniques taking high-concentration properties into account must be used when determining force field model parameters, or that the class of models considered here is intrinsically incapable of the task and more sophisticated mathematical forms must be used.

Molecular simulation of aqueous electrolyte solubility. 3. Alkali-halide salts and their mixtures in water and in hydrochloric acid.

We extend the osmotic ensemble Monte Carlo (OEMC) molecular simulation method (Moučka et al. J. Phys Chem. B 2011, 115, 7849-7861) for directly calculating the aqueous solubility of electrolytes and for calculating their chemical potentials as functions of concentration to cases involving electrolyte hydrates and mixed electrolytes, including invariant points involving simultaneous precipitation of several solutes. The method utilizes a particular semigrand canonical ensemble, which performs simulations of the solution at a fixed number of solvent molecules, pressure, temperature, and specified overall electrolyte chemical potential. It avoids calculations for the solid phase, incorporating available solid chemical potential data from thermochemical tables, which are based on well-defined reference states, or from other sources. We apply the method to a range of alkali halides in water and to selected examples involving LiCl monohydrate, mixed electrolyte solutions involving water and hydrochloric acid, and invariant points in these solvents. The method uses several existing force-field models from the literature, and the results are compared with experiment. The calculated results agree qualitatively well with the experimental trends and are of reasonable accuracy. The accuracy of the calculated solubility is highly dependent on the solid chemical potential value and also on the force-field model used. Our results indicate that pairwise additive effective force-field models developed for the solution phase are unlikely to also be good models for the corresponding crystalline solid. We find that, in our OEMC simulations, each ionic force-field model is characterized by a limiting value of the total solution chemical potential and a corresponding aqueous concentration. For higher values of the imposed chemical potential, the solid phase in the simulation grows in size without limit.

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

ABSTRACT Although aqueous electrolytes are among the most important solutions, the molecular simulation of their intertwined properties of chemical potentials, solubility and activity coefficients has remained a challenging problem, and has attracted considerable recent interest. In this perspectives review, we focus on the simplest case of aqueous sodium chloride at ambient conditions and discuss the two main factors that have impeded progress. The first is lack of consensus with respect to the appropriate methodology for force field (FF) development. We examine how most commonly used FFs have been developed, and emphasise the importance of distinguishing between ‘Training Set Properties’ used to fit the FF parameters, and ‘Test Set Properties’, which are pure predictions of additional properties. The second is disagreement among solubility results obtained, even using identical FFs and thermodynamic conditions. Solubility calculations have been approached using both thermodynamic-based methods and direct molecular dynamics-based methods implementing coexisting solution and solid phases. Although convergence has been very recently achieved among results based on the former approach, there is as yet no general agreement with simulation results based on the latter methodology. We also propose a new method to directly calculate the electrolyte standard chemical potential in the Henry law ideality model. We conclude by making recommendations for calculating solubility, chemical potentials and activity coefficients, and outline a potential path for future progress.

Molecular simulation of aqueous electrolytes: water chemical potential results and Gibbs-Duhem equation consistency tests.

This paper deals with molecular simulation of the chemical potentials in aqueous electrolyte solutions for the water solvent and its relationship to chemical potential simulation results for the electrolyte solute. We use the Gibbs-Duhem equation linking the concentration dependence of these quantities to test the thermodynamic consistency of separate calculations of each quantity. We consider aqueous NaCl solutions at ambient conditions, using the standard SPC/E force field for water and the Joung-Cheatham force field for the electrolyte. We calculate the water chemical potential using the osmotic ensemble Monte Carlo algorithm by varying the number of water molecules at a constant amount of solute. We demonstrate numerical consistency of these results in terms of the Gibbs-Duhem equation in conjunction with our previous calculations of the electrolyte chemical potential. We present the chemical potential vs molality curves for both solvent and solute in the form of appropriately chosen analytical equations fitted to the simulation data. As a byproduct, in the context of the force fields considered, we also obtain values for the Henry convention standard molar chemical potential for aqueous NaCl using molality as the concentration variable and for the chemical potential of pure SPC/E water. These values are in reasonable agreement with the experimental values.

Chemical Potentials, Activity Coefficients, and Solubility in Aqueous NaCl Solutions: Prediction by Polarizable Force Fields

We describe a computationally efficient molecular simulation methodology for calculating the concentration dependence of the chemical potentials of both solute and solvent in aqueous electrolyte solutions, based on simulations of the salt chemical potential alone. We use our approach to study the predictions for aqueous NaCl solutions at ambient conditions of these properties by the recently developed polarizable force fields (FFs) AH/BK3 of Kiss and Baranyai (J. Chem. Phys. 2013, 138, 204507) and AH/SWM4-DP of Lamoureux and Roux (J. Phys. Chem. B 2006, 110, 3308 - 3322) and by the nonpolarizable JC FF of Joung and Cheatham tailored to SPC/E water (J. Phys. Chem. B 2008, 112, 9020 - 9041). We also consider their predictions of the concentration dependence of the electrolyte activity coefficient, the crystalline solid chemical potential, the electrolyte solubility, and the solution specific volume. We first highlight the disagreement in the literature concerning calculations of solubility by means of molecular simulation in the case of the JC FF and provide strong evidence of the correctness of our methodology based on recent independently obtained results for this important test case. We then compare the predictions of the three FFs with each other and with experiment and draw conclusions concerning their relative merits, with particular emphasis on the salt chemical potential and activity coefficient vs concentration curves and their derivatives. The latter curves have only previously been available from Kirkwood-Buff integrals, which require approximate numerical integrations over system pair correlation functions at each concentration. Unlike the case of the other FFs, the AH/BK3 curves are nearly parallel to the corresponding experimental curves at moderate and higher concentrations. This leads to an excellent prediction of the water chemical potential via the Gibbs-Duhem equation and enables the activity coefficient curve to be brought into excellent agreement with experiment by incorporating an appropriate value of the standard state chemical potential in the Henry Law convention.

Molecular Force Field Development for Aqueous Electrolytes: 1. Incorporating Appropriate Experimental Data and the Inadequacy of Simple Electrolyte Force Fields Based on Lennard-Jones and Point Charge Interactions with Lorentz−Berthelot Rules

It is known that none of the available simple molecular interaction models of aqueous electrolytes based on SPC/E water and their associated force fields are able to reproduce the concentration dependence of important thermodynamic properties of even the simplest electrolyte, NaCl, at ambient conditions over the entire experimentally accessible concentration range [ Mouc̆ka , F. ; Nezbeda , I. ; Smith , W. R. J. Chem. Phys. 2013 , 138 , 154102 ]. This paper explores the possibility of improving their performance by incorporating concentration-dependent experimental data for the total ionic chemical potential and the density into the fitting procedure, in addition to experimental values of solubility and solid chemical potential. We describe a general parameter estimation methodology for a studied class of models that incorporates the aforementioned experimental data. When the entire concentration range is considered, although the resulting force field is a slight improvement over others currently available in the literature, overall quantitative agreement with the experimental data over this range remains unsatisfactory. This indicates an inherent limitation of such simple molecular interaction models and strongly suggests that more complex mathematical forms of such models are required to quantitatively predict the properties of aqueous electrolyte solutions when the entire concentration range is of interest. Our parameter estimation methodology is also applicable to such cases.

Efficient multiparticle sampling in Monte Carlo simulations on fluids: application to polarizable models.

A novel Monte Carlo simulation scheme based on biased simultaneous displacements of all particles of the system has been developed. The method is particularly suited for systems with nonadditive interactions and its efficiency is demonstrated by its implementation for the polarizable Stockmayer fluid. Performance of the method is compared with both the standard one-particle move method and an unbiased multiparticle scheme by computing the mean squared displacements, rotation relaxation, and the speed of equilibration (translational order parameter). It is shown that the proposed biased method is about a factor of 10 faster, for the system considered, when compared with the other schemes.

Computationally efficient Monte Carlo simulations for polarisable models: multi-particle move method for water and aqueous electrolytes

We demonstrate improved computational efficiencies of Monte Carlo (MC) simulations for polarisable force fields by implementing the multi-particle-move MC (MPM-MC) method [Moučka F, Rouha M, Nezbeda I. Efficient multiparticle sampling in Monte Carlo simulations on fluids: application to polarizable models. J Phys Chem. 2007;126:224106]. Force bias and smart alternatives along with the Ewald summation and generalised reaction field have been considered and tested for both pure polarisable water models and polarisable aqueous electrolytes. For water, we consider the recently developed Baranyai–Kiss force field [A transferable classical potential for the water molecule. J Chem Phys. 2010;133:144109] and the SWM4-DP force field of Lamoureux et al. [A simple polarizable model of water based on classical Drude oscillators. J Chem Phys. 2003;119:5185], and for electrolytes the polarisable AH/SWM4-DP force field associated with the SWM4-DP solvent. These force fields incorporate polarisability as a charge-on-spring model, and the Baranyai–Kiss model incorporates charges in the form of a Gaussian distribution instead of point charges. For neat water, in addition to calculating the standard thermodynamic properties and water structure and comparing our results with those obtained from standard molecular dynamics simulations, we also investigate its vapour–liquid equilibrium properties. For aqueous electrolyte solutions, we study NaCl at ambient conditions and calculate its density and chemical potential as a function of concentration, representing apparently the first such simulation results using these polarisable models at finite concentrations. Our results demonstrate that MC simulations can be efficiently performed on polarisable models if the MPM method is incorporated.

Vapor–Liquid Equilibrium and Polarization Behavior of the GCP Water Model: Gaussian Charge-on-Spring versus Dipole Self-Consistent Field Approaches to Induced Polarization

We developed the Gaussian charge-on-spring (GCOS) version of the original self-consistent field implementation of the Gaussian Charge Polarizable water model and test its accuracy to represent the polarization behavior of the original model involving smeared charges and induced dipole moments. For that purpose we adapted the recently proposed multiple-particle-move (MPM) within the Gibbs and isochoric-isothermal ensembles Monte Carlo methods for the efficient simulation of polarizable fluids. We assessed the accuracy of the GCOS representation by a direct comparison of the resulting vapor-liquid phase envelope, microstructure, and relevant microscopic descriptors of water polarization along the orthobaric curve against the corresponding quantities from the actual GCP water model.