Truncation of Coulombic interactions in computer simulations of liquids

Assessment of the Wolf method using the Stillinger-Lovett sum rules: From strong electrolytes to weakly charged colloidal dispersions

The Ewald method has been the cornerstone in molecular simulations for modeling electrostatic interactions of charge-stabilized many-body systems. In the late 1990s, Wolf and collaborators developed an alternative route to describe the long-range nature of electrostatic interactions; from a computational perspective, this method provides a more efficient and straightforward way to implement long-range electrostatic interactions than the Ewald method. Despite these advantages, the validity of the Wolf potential to account for the electrostatic contribution in charged fluids remains controversial. To alleviate this situation, in this contribution, we implement the Wolf summation method to both electrolyte solutions and charged colloids with moderate size and charge asymmetries in order to assess the accuracy and validity of the method. To this end, we verify that the proper selection of parameters within the Wolf method leads to results that are in good agreement with those obtained through the standard Ewald method and the theory of integral equations of simple liquids within the so-called hypernetted chain approximation. Furthermore, we show that the results obtained with the original Wolf method do satisfy the moment conditions described by the Stillinger-Lovett sum rules, which are directly related to the local electroneutrality condition and the electrostatic screening in the Debye-Hückel regime. Hence, the fact that the solution provided by the Wolf method satisfies the first and second moments of Stillinger-Lovett proves, for the first time, the reliability of the method to correctly incorporate the electrostatic contribution in charge-stabilized fluids. This makes the Wolf method a powerful alternative compared to more demanding computational approaches.

Electrostatic interactions in soft particle systems: mesoscale simulations of ionic liquids

Computer simulations provide a unique insight into the microscopic details, molecular interactions and dynamic behavior responsible for many distinct physicochemical properties of ionic liquids. Due to the sluggish and heterogeneous dynamics and the long-ranged nanostructured nature of ionic liquids, coarse-grained meso-scale simulations provide an indispensable complement to detailed first-principles calculations and atomistic simulations allowing studies over extended length and time scales with a modest computational cost. Here, we present extensive coarse-grained simulations on a series of ionic liquids of the 1-alkyl-3-methylimidazolium (alkyl = butyl, heptyl-, and decyl-) family with Cl, [BF4], and [PF6] counterions. Liquid densities, microstructures, translational diffusion coefficients, and re-orientational motion of these model ionic liquid systems have been systematically studied over a wide temperature range. The addition of neutral beads in cationic models leads to a transition of liquid morphologies from dispersed apolar beads in a polar framework to that characterized by bi-continuous sponge-like interpenetrating networks in liquid matrices. Translational diffusion coefficients of both cations and anions decrease upon lengthening of the neutral chains in the cationic models and by enlarging molecular sizes of the anionic groups. Similar features are observed in re-orientational motion and time scales of different cationic models within the studied temperature range. The comparison of the liquid properties of the ionic systems with their neutral counterparts indicates that the distinctive microstructures and dynamical quantities of the model ionic liquid systems are intrinsically related to Coulombic interactions. Finally, we compared the computational efficiencies of three linearly scaling O(N log N) Ewald summation methods, the particle-particle particle-mesh method, the particle-mesh Ewald summation method, and the Ewald summation method based on a non-uniform fast Fourier transform technique, to calculate electrostatic interactions. Coarse-grained simulations were performed using the GALAMOST and the GROMACS packages and hardware efficiently utilizing graphics processing units on a set of extended [1-decyl-3-methylimidazolium][BF4] ionic liquid systems of up to 131 072 ion pairs.

Toward the correction of effective electrostatic forces in explicit-solvent molecular dynamics simulations: restraints on solvent-generated electrostatic potential and solvent polarization

Despite considerable advances in computing power, atomistic simulations under nonperiodic boundary conditions, with Coulombic electrostatic interactions and in systems large enough to reduce finite-size associated errors in thermodynamic quantities to within the thermal energy, are still not affordable. As a result, periodic boundary conditions, systems of microscopic size and effective electrostatic interaction functions are frequently resorted to. Ensuing artifacts in thermodynamic quantities are nowadays routinely corrected a posteriori, but the underlying configurational sampling still descends from spurious forces. The present study addresses this problem through the introduction of on-the-fly corrections to the physical forces during an atomistic molecular dynamics simulation. Two different approaches are suggested, where the force corrections are derived from special potential energy terms. In the first approach, the solvent-generated electrostatic potential sampled at a given atom site is restrained to a target value involving corrections for electrostatic artifacts. In the second approach, the long-range regime of the solvent polarization around a given atom site is restrained to the Born polarization, i.e., the solvent polarization corresponding to the ideal situation of a macroscopic system under nonperiodic boundary conditions and governed by Coulombic electrostatic interactions. The restraints are applied to the explicit-water simulation of a hydrated sodium ion, and the effect of the restraints on the structural and energetic properties of the solvent is illustrated. Furthermore, by means of the calculation of the charging free energy of a hydrated sodium ion, it is shown how the electrostatic potential restraint translates into the on-the-fly consideration of the corresponding free-energy correction terms. It is discussed how the restraints can be generalized to situations involving several solute particles. Although the present study considers a very simple system only, it is an important step toward the on-the-fly elimination of finite-size and approximate-electrostatic artifacts during atomistic molecular dynamics simulations.

Cutoff radius effect of the isotropic periodic sum and Wolf method in liquid-vapor interfaces of water

As a more economical but similarly accurate computation method than the Ewald sum, the isotropic periodic sum (IPS) method for nonpolar molecules (IPSn) and polar molecules (IPSp), along with the Wolf method are of interest, but the cutoff radius dependence is an important issue. To evaluate the cutoff radius effect of the three methods, a water-vapor interfacial system has been studied by molecular dynamics. The Wolf method can produce adequate results for surface tension compared to that of the Ewald sum (within 2.9%) at a long enough cutoff radius, r(c). However, the estimation of the electrostatic potential profile and dipole orientational function is poor. The Wolf method cannot estimate electrostatic configuration at r(c) ≤ L(z)∕2 (L(z) is the longest lattice of the system). We have found that the convergence of the surface tension and the electrostatic configuration of the IPSn method is faster than that of the IPSp method. Moreover, the IPSn method is most accurate among the three methods for the same cutoff radius. Furthermore, the behavior of the surface tension against the cutoff radius shows a greater difference for the IPSn and IPSp method. The surface tension of the IPSp method fluctuates and presents a similar result to that of the Ewald sum, but the surface tension for the IPSn method greatly deviates near r(c) = L(z)∕3. The cause of this deviation is the difference between the interfacial configuration of the water surface and the cutoff treatment of the IPS method. The deviation becomes insignificant far from r(c) = L(z)∕3. In spite of this shortcoming, the IPSn method gives the most accurate result in estimating the surface tension at r(c) = L(z)∕2. From all the results in this work, the IPSn and IPSp method have been found to be more accurate than the Wolf method. In conclusion, the surface tension and structure of water-vapor interface can be calculated by the IPSn method when r(c) is greater than or equal to the longest lattice of the system. The IPSp method and the Wolf method require a longer cutoff radius than the longest lattice of the system to estimate interfacial properties.

Nondielectric long-range solvation of polar liquids in cubic symmetry

Long-range solvation properties of strongly coupled dipolar systems simulated using the Ewald and reaction field methods are assessed by using electric fluctuation formulas for a dielectric medium. Some components of the fluctuating electric multipole moments are suppressed, whereas other components are favored as the boundary of the simulation box is approached. An analysis of electrostatic interactions in a periodic cubic system suggests that these structural effects are due to the periodicity embedded in the Ewald method. Furthermore, the results obtained using the reaction field method are very similar to those obtained using the Ewald method, an effect which we attribute to the use of toroidal boundary conditions in the former case. Thus, the long-range solvation properties of polar liquids simulated using either of the two methods are nondielectric in their character.

Molecular dynamics simulations of a reversibly folding beta-heptapeptide in methanol: influence of the treatment of long-range electrostatic interactions

Eight 100-ns molecular dynamics simulations of a beta-heptapeptide in methanol at 340 K (within cubic periodic computational boxes of about 6-nm edge) are reported and compared. These simulations were performed with three different charge-state combinations at the peptide termini, one of them with or without a neutralizing chloride counterion, and using either the lattice-sum (LS) or reaction-field (RF) scheme to handle electrostatic interactions. The choice of the electrostatic scheme has essentially no influence on the folding-unfolding equilibrium when the peptide termini are uncharged and only a small influence when the peptide is positively charged at its N-terminus (with or without inclusion of a neutralizing chloride counterion). However, when the peptide is zwitterionic, the LS scheme leads to preferential sampling of the high-dipole folded helical state, whereas the RF scheme leads to preferential sampling of a low-dipole unfolded salt-bridged state. A continuum electrostatics analysis based on the sampled configurations (zwitterionic case) suggests that the LS scheme stabilizes the helical state through artificial periodicity, but that the magnitude of this perturbation is essentially negligible (compared to the thermal energy) for the large box size and relatively polar solvent considered. The results thus provide clear evidence (continuum electrostatics analysis) for the absence of LS artifacts and some indications (still not definitive because of the limited sampling of the folding-unfolding transition) for the presence of RF artifacts in this specific system.

Dressed ion theory of size-asymmetric electrolytes: Effective ionic charges and the decay length of screened Coulomb potential and pair correlations

The effects of ionic size asymmetry on long-range electrostatic interactions in electrolyte solutions are investigated within the primitive model. Using the formalism of dressed ion theory we analyze correlation functions from Monte Carlo simulations and the hypernetted chain approximation for size asymmetric 1:1 electrolytes. We obtain decay lengths of the screened Coulomb potential, effective charges of ions, and effective permittivity of the solution. It is found that the variation of these quantities with the degree of size asymmetry depends in a quite intricate manner on the interplay between the electrostatic coupling and excluded volume effects. In most cases the magnitude of the effective charge of the small ion species is larger than that of the large species; the difference increases with increasing size asymmetry. The effective charges of both species are larger (in absolute value) than the bare ionic charge, except for high asymmetry where the effective charge of the large ions can become smaller than the bare charge.

Two-dimensional Monte Carlo simulations of ionic and nonionic silane self-assembly on hydrophilic surfaces

Aqueous chemistries have recently been shown to be useful for the deposition of hydrophobic films of nonionic and cationic silanes on hydrophilic substrates for the prevention of stiction in MEMS. The Monte Carlo method is used to simulate in two dimensions the self-assembly of silane films on a hydrophilic surface. We investigate the impact of charged group in cationic silane on the overall structure of the films. We characterize the film structure with spatial pair correlations at each molecular layer of the deposited films. The simulations reveal long-range correlations for the film of cationic silanes. Based on our two-dimensional simulations, we report an average "most probable" structure for the films of nonionic and cationic silanes.

Computer simulations with explicit solvent: recent progress in the thermodynamic decomposition of free energies and in modeling electrostatic effects

This review focuses on recent progress in two areas in which computer simulations with explicit solvent are being applied: the thermodynamic decomposition of free energies, and modeling electrostatic effects. The computationally intensive nature of these simulations has been an obstacle to the systematic study of many problems in solvation thermodynamics, such as the decomposition of solvation and ligand binding free energies into component enthalpies and entropies. With the revolution in computer power continuing, these problems are ripe for study but require the judicious choice of algorithms and approximations. We provide a critical evaluation of several numerical approaches to the thermodynamic decomposition of free energies and summarize applications in the current literature. Progress in computer simulations with explicit solvent of charge perturbations in biomolecules was slow in the early 1990s because of the widespread use of truncated Coulomb potentials in these simulations, among other factors. Development of the sophisticated technology described in this review to handle the long-range electrostatic interactions has increased the predictive power of these simulations to the point where comparisons between explicit and continuum solvent models can reveal differences that have their true physical origin in the inherent molecularity of the surrounding medium.

Monte-Carlo-self consistent field method in the polyelectrolyte theory

A new time saving numerical method for calculation of equilibrium potential and density distribution of mobile ions around the polyion in a polyelectrolyte system is proposed: the region around the polyion is being divided into two zones-internal and external; in the internal zone all the ions are accounted explicity with the aid of Monte-Carlo procedure; in the external zone the combined Monte-Carlo-self consistent field method proposed earlier is applied, an exchange of ions between regions is being implied. For 1:1 electrolyte the optimal choice of the boundary between the zones has been demonstrated. As an example of a more complicated system calculation for 2:2:1:1 electrolyte was carried out.