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Molecular simulations in an open environment, involving ion exchange, are necessary to study various systems, from biosystems to confined electrolytes. However, grand-canonical simulations are often computationally demanding in condensed phases. A promising method [L. Belloni, J. Chem. Phys. 151, 021101 (2019)], one of the hybrid nonequilibrium molecular dynamics/Monte Carlo algorithms, was recently developed, which enables efficient computation of fluctuating number or charge density in dense fluids or ionic solutions. This method facilitates the exchange through an auxiliary dimension, orthogonal to all physical dimensions, by reducing initial steric and electrostatic clashes in three-dimensional systems. Here, we report the implementation of the method in LAMMPS with a Python interface, allowing facile access to grand-canonical molecular dynamics simulations with massively parallelized computation. We validate our implementation with two electrolytes, including a model Lennard-Jones electrolyte similar to a restricted primitive model and aqueous solutions. We find that electrostatic interactions play a crucial role in the overall efficiency due to their long-range nature, particularly for water or ion-pair exchange in aqueous solutions. With properly screened electrostatic interactions and bias-based methods, our approach enhances the efficiency of salt-pair exchange in Lennard-Jones electrolytes by approximately four orders of magnitude, compared to conventional grand-canonical Monte Carlo. Furthermore, the acceptance rate of NaCl-pair exchange in aqueous solutions at moderate concentrations reaches about 3% at the maximum efficiency. [ABSTRACT FROM AUTHOR]

This paper assesses the ability of molecular density functional theory to predict efficiently and accurately the hydration free energies of molecular solutes and the surrounding microscopic water structure. A wide range of solutes were investigated, including hydrophobes, water as a solute, and the FreeSolv database containing 642 drug-like molecules having a variety of shapes and sizes. The usual second-order approximation of the theory is corrected by a third-order, angular-independent bridge functional. The overall functional is parameter-free in the sense that the only inputs are bulk water properties, independent of the solutes considered. These inputs are the direct correlation function, compressibility, liquid–gas surface tension, and excess chemical potential of the solvent. Compared to molecular simulations with the same force field and the same fixed solute geometries, the present theory is shown to describe accurately the solvation free energy and structure of both hydrophobic and hydrophilic solutes. Overall, the method yields a precision of order 0.5 kBT for the hydration free energies of the FreeSolv database, with a computer speedup of 3 orders of magnitude. The theory remains to be improved for a better description of the H-bonding structure and the hydration free energy of charged solutes. [ABSTRACT FROM AUTHOR]

The capability of molecular density functional theory in its lowest, second-order approximation, equivalent to the hypernetted chain approximation in integral equations, to predict accurately the hydration free-energies and microscopic structure of molecular solutes is explored for a variety of systems: spherical hydrophobic solutes, ions, water as a solute, and the Mobley's dataset of organic molecules. The successes and the caveats of the approach are carefully pinpointed. Compared to molecular simulations with the same force field and the same fixed solute geometries, the theory describes accurately the solvation of cations, less so that of anions or generally H-bond acceptors. Overall, the electrostatic contribution to solvation free-energies of neutral molecules is correctly reproduced. On the other hand, the cavity contribution is poorly described but can be corrected using scaled-particle theory ideas. Addition of a physically motivated, one-parameter cavity correction accounting for both pressure and surface effects in the nonpolar solvation contribution yields a precision of 0.8 kcal/mol for the overall hydration free energies of the whole Mobley's dataset. Inclusion of another one-parameter cavity correction for the electrostatics brings it to 0.6 kcal/mol, that is, kBT. This is accomplished with a three-orders of magnitude numerical speed-up with respect to molecular simulations. [ABSTRACT FROM AUTHOR]

The process of inserting/deleting a particle during grand-canonical Monte-Carlo (MC) simulations is investigated using a novel, original technique: the trial event is made of a short nonequilibrium molecular dynamics (MD) trajectory during which a coordinate w along a 4th dimension is added to the particle in the course of insertion/deletion and is forced to decrease from large values down to zero (for insertion) or increased from 0 up to large values (for extraction) at imposed vw velocity. The probability of acceptation of the whole MC move is controlled by the chemical potential and the external work applied during the trajectory. Contrary to the standard procedures which create/delete suddenly a particle, the proposed technique gives time to the fluid environment to relax during the gradual insertion/extraction before the acceptation decision. The reward for this expensive trial move is a gain of many orders of magnitude in the success rate. The power and wide domain of interest of this hybrid "H4D" algorithm which marries stochastic MC and nonequilibrium deterministic MD flavors are briefly illustrated with hard sphere, water, and electrolyte systems. The same approach can be easily adapted in order to measure the chemical potential of a solute particle immersed in a fluid during canonical or isobaric simulations. It then becomes an efficient application of the Jarzynski theorem for the determination of solvation free energy. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations of dipolar fluids are performed at different numbers of particles N = 100-4000. For each size of the cubic cell, the non-spherically symmetric pair distribution function g(r,Ω) is accumulated in terms of projections gmnl(r) onto rotational invariants. The observed N dependence is in very good agreement with the theoretical predictions for the finite-size corrections of different origins: the explicit corrections due to the absence of fluctuations in the number of particles within the canonical simulation and the implicit corrections due to the coupling between the environment around a given particle and that around its images in the neighboring cells. The latter dominates in fluids of strong dipolar coupling characterized by low compressibility and high dielectric constant. The ability to clean with great precision the simulation data from these corrections combined with the use of very powerful anisotropic integral equation techniques means that exact correlation functions both in real and Fourier spaces, Kirkwood-Buff integrals, and bridge functions can be derived from box sizes as small as N ≈ 100, even with existing long-range tails. In the presence of dielectric discontinuity with the external medium surrounding the central box and its replica within the Ewald treatment of the Coulombic interactions, the 1/N dependence of the gmnl(r) is shown to disagree with the, yet well-accepted, prediction of the literature. [ABSTRACT FROM AUTHOR]

The exact molecular bridge function of the extended simple point charge model of liquid water at room temperature is extracted from Monte Carlo (MC) simulation data. The projections gμνmnl(r) onto rotational invariants of the highly directional pair distribution function g(r,Ω) are accumulated during simulation performed with N = 512 molecules (cubic box size L ≈ 25 Å). Making intensive use of anisotropic integral equation techniques, the molecular Ornstein-Zernike equation fed with the MC data available at short distances and completed beyond L/2 with the hypernetted chain closure valid at long distances is then inverted in order to derive on the whole r range the direct correlation function cμνmnl(r), the cavity function yμνmnl(r), the negative excess potential of mean force lnyμνmnl(r), and, finally, the holy grail in such liquid state theory, the bridge function bμνmnl(r) projections. For completeness, the short distance domain inside the soft core can be reached, thanks to the use of a specially designed anisotropic finite potential which replaces the true one between a single pair of molecules in the simulation. The final bridge function b(r,Ω) of bulk water presents strong, non-universal directional features and can now serve as a reference for approximated bridge functions or functionals in liquid physics of aqueous solvents and solutions. [ABSTRACT FROM AUTHOR]

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r, Ω) around the solute is a function of the position r ≡ (x, y, z) and of the three Euler angles Ω (ϑ, ∅, ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r, Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes.We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water. [ABSTRACT FROM AUTHOR]

The exact bridge function of the Lennard-Jones dipolar (Stockmayer) fluid is extracted from Monte Carlo simulation data. The projections gmnl(r) onto rotational invariants of the non-spherically symmetric pair distribution function g(r, Ω) are accumulated during simulation. Making intensive use of anisotropic integral equation techniques, the molecular Ornstein-Zernike equation is then inverted in order to derive the direct correlation function cmnl(r), the cavity function ymnl(r), the negative excess potential of mean force lny|mnl(r), and the bridge function bmnl(r) projections. b(r, Ω) presents strong, non-universal anisotropies at high dipolar coupling. This simulation data analysis may serve as reference and guide for approximated bridge function theories of dipolar fluids and is a valuable step towards the case of more refined, nonlinear water-like geometries. [ABSTRACT FROM AUTHOR]

Recent analyses of sedimentation profiles in charged colloidal suspensions are examined in view of general, somewhat underestimated, concepts. It is recalled that the standard equation for osmotic pressure equilibrium, which involves pair correlations between colloids only, remains valid in the presence of long-range Coulombic interactions. The entropy of the counterions and the electric field generated by the spatial inhomogeneity are implicitly taken into account in the colloid structure factor through the compressibility equation and local electroneutrality conditions. Limiting the macroscopic analysis to the pure electric-field contribution or, equivalently, to the ideal ionic pressure, corresponds to the incorrect, bare Debye-Hückel approximation for the colloid-colloid correlations. A one-component description with reasonable Derjaguin-Landau-Verwey-Overbeek-type ion-averaged effective pair potential between colloids is sufficient to derive the sedimentation profile of highly charged, weakly screened colloidal suspensions. The macroscopic electric field is directly related to the microscopic electrostatic potential around the colloids. [ABSTRACT FROM AUTHOR]

The structure and fluctuations of the swollen Lα lamellar phase of highly charged surfactant didodecyldimethylammonium halide fluid bilayers (DDA+X-) are studied using high-resolution small-angle x-ray scattering and medium-resolution, high-contrast small-angle neutron-scattering. The Caillé parameter η, as a function of the swelling (Lα periodicity d), was determined from the full q-range fits of the measured scattering profiles for three different counterions (X-=Cl-, Br-, and NO3-). This parameter quantifies the amplitude of the membrane fluctuations within the Landau–de Gennes smectic-A linear elasticity theory. The different anions used gave strong specific effects at the maximum swelling of the Lα phase, while at lower swellings a two-phase coexistence of swollen and collapsed lamellae (d∼30 and ∼80 Å) was observed for bromide and nitrate ions. Over the intermediate dilution range for all three counterions, a single Lα phase can be continuously swollen with pure water which is governed by an equation of state (i.e., osmotic pressure versus period) and thermally excited fluctuation amplitudes that can be well described by the same Poisson–Boltzmann calculation. The membranes were found to be slightly stiffer than predicted by purely electrostatic repulsions, and this is tentatively attributed to an extra bending rigidity contribution from the surfactant chains. [ABSTRACT FROM AUTHOR]

Concentration up to about 1M describes the osmotic coefficients of a series of 16 aqueous electrolyte solutions. Although the description of bulk properties is satisfactory, prediction of surface tensions of the corresponding solutions (hotmeister series) is not very successful.

Studies the integral equation theory of flexible polyelectrolytes using the Primitive Model approach. Description of the system; Results for a typical salt free binary semidilute system; Influence of the monomer concentration on the properties of the system.

The influence of 1-hexanol on the structural changes of dodecyltrimethylammonium bromide (C12TAB) solutions that contain from 0.02 to 0.20 M of surfactant and up to equimolar concentrations of alcohol and surfactant is discussed. It is concluded that most of the results on C12TAB and its mixtures with 1-hexanol, known from literature, could be confirmed.

The hypernetted chain (HNC) integral equation is solved for a variety of systems including the simple fluid of hard spheres with attractive Yukawa tail, the symmetrical and highly asymmetrical mixtures of charged particles, and the mixtures of hard spheres with positively nonadditive diameters. All these systems exhibit a liquid–gas or fluid–fluid phase separation. We are concerned with the behavior of the HNC solution near the two-phase region in the phase diagram. In all cases, the HNC equation does not have solutions inside a certain region whose boundary line is not a spinodal line. As the boundary is approached, the isothermal compressibility deduced from the compressibility route does not diverge, but tends to finite values. The isotherms and isochores terminate at the boundary line in square root branch points. This behavior is directly correlated to the existence of multiple HNC solutions. Physical and nonphysical solutions coincide on the boundary line. This universal HNC behavior is compared with that of the mean spherical approximation and Percus–Yevick integral equations. [ABSTRACT FROM AUTHOR]

We introduce a new statistical-mechanical model of the surface charge process in colloidal suspensions. The chemical adsorption of ions on the surface is described with a narrow and deep well in the pair potential between the spherical colloids and the ions. This extends the Cummings and Stell model of bulk chemical reactions. In this simple case of association of spherically symmetric atoms into diatomic molecules, we verify that the model fulfils the law of mass action involving the activities of the reactant and product particles. In the case of surface reactions, we solve numerically the hypernetted-chain integral equation for the equilibrium properties of the system. From the pair distribution functions we deduce the implicit structural charge of the colloid as well as the electrostatic condensation of the counter ions, the ion–ion correlations inside the chemical shell and the colloid–colloid effective repulsion. [ABSTRACT FROM AUTHOR]

We apply the mixed integral equation (ZH) proposed recently by Zerah and Hansen to highly asymmetrical polyelectrolytes within the primitive model. The closure interpolates continuously between the Percus–Yevick and the hypernetted chain closures for charges of same sign and between the HNC and mean spherical approximations for charges of opposite sign. The thermodynamic consistency between the virial and compressibility equations of state is obtained by varying the single parameter in the switching functions. In weakly screened and highly charged suspensions, the new ZH equation improves appreciably the HNC results. The structure factors are essentially modified in the infinite wavelength limit. The two-phase region in the phase diagram is shifted towards the low temperature or the high charge region which allows us to study more asymmetrical systems than with the HNC equation. Since no simulation data are available, the ZH equation is useful to quantify the accuracy of the HNC closure for such systems. [ABSTRACT FROM AUTHOR]