Electrostatic Interaction Model Research Articles

Effective dipole model for electrostatic interactions between polarizable spherical particles in particle scale simulations

Despite their widespread adoption, particle-scale simulation methods, such as the Discrete Element Method (DEM), for electrically charged particles in several natural processes and industrial transformations do not include realistic polarization effects. At close distances, these can dominate the particle motion and are impossible to predict by the commonly adopted Coulomb point-charge approximation. Sophisticated mathematical tools can account for uneven charge distributions, predicting an attractive force between a charged particle and a neutral particle or possible attraction between two like-charged particles. Such approaches are accurate but too complex for implementation in DEM simulations of many interacting particles. We propose a novel, simpler yet realistically accurate effective dipole model. By attributing a net charge and an induced effective dipole to each sphere, the interaction force between charged polarizable particles is computed in closed form. A comparison of a rigorous solution and the proposed dipole approach for two spherical particles reveals significant improvement over the commonly employed Coulomb law. The effects of particle size ratio and charge ratio on the interaction force are discussed. Then, the dynamic DEM simulation of a shaker filled with a binary mixture of differently sized particles that are all positively charged is shown to predict the counterintuitive formation of fine-on-coarse aggregates.

Solvent effects on the prediction of redox potentials: Application to nitroxides

This paper investigates the impact of solute-solvent interactions on the redox potentials of nitroxides, with a focus on ionic interactions caused by the presence of electrolytes found in different environment such as batteries. The analysis of various nitroxide families shows that ion-substituent interactions, especially in aromatic systems, significantly influence complex stability. Indeed, the counterion typically prefers to position near the substituent. However, in acetonitrile, the hydroxylamine anion and its cation show strong interactions when the cation is near the nitroxyl moiety. The study also confirm that an electrostatic interaction model can predict the effects of substituents, aromaticity, and ring size on redox potentials of nitroxides. Concerning the impact of the environment, solute-ion interactions and ion-pairs formation play a crucial role in modulating the redox potential.

Validity of an approximate electrostatic interaction model

We explain the reasons why a simple approximate expression for the interaction energy between two parallel uniformly charged wires works so well for the calculation of the stored electrostatic energy of a uniformly charged square and/or rectangular plate. The expression under consideration was also found to be very accurate when calculating the total energy of a model consisting of an arbitrary number of uniformly charged wires placed parallel to each other along a one-dimensional regular lattice when the number of wires is not very small. One can use the derived approximate expression for the interaction energy instead of the more elaborate exact one in all circumstances where there is no need for an extremely high accuracy.

Analysis of infinite plane assumption and point charge assumption in the particle–plane electrostatic interaction model by re-expansion method and image multipole method

The solutions for the electrostatic interacting force between a particle and a plane typically assume that the plane is infinite and the particle can be approximated as a point charge. Nevertheless, the prerequisites of underlying assumptions of these calculations remain unspecified, resulting in the inability to assess the reliability of the results and constraining the practical applicability of analytical models. In this paper, the authors introduce the particle–coated plane electrostatic interaction model by employing the re-expansion method. Additionally, the multipole–coated plane electrostatic interaction model is presented using the image multipole method. An analysis of the assumptions’ prerequisites is conducted, considering a relative error of less than 2 % as the approximate standard. The findings indicate that, irrespective of the material properties of the particle and plane, the radius of the planar plate must exceed three times the distance between the particle’s center and the plane to satisfy the infinite plane assumption. When the distance between the particle’s center and the plane surpasses three times the radius, it is permissible to approximate the charged particle as a point charge. The study presented in this paper establishes a standard for prior estimation of the departure range in existing analytical models related to particle–plane electrostatic interaction. This work also serves as a theoretical basis for the practical application of these models in engineering.

Charge-Optimized Electrostatic Interaction Atom-Centered Neural Network Algorithm.

Machine-learning algorithms have been proposed to capture electrostatic interactions by using effective partial charges. These algorithms often rely on a pretrained model for partial charge prediction using density functional theory-calculated partial charges as references, which introduces complexity to the force field model. The accuracy of the trained model also depends on the reliability of charge partition methods, which can be dependent on the specific system and methodology employed. In this study, we propose an atom-centered neural network (ANN) algorithm that eliminates the need for reference charges. Our algorithm requires only a single NN model for each element to obtain both atomic energy and charges. These atomic charges are then employed to compute electrostatic energies using the Ewald summation algorithm. Subsequently, the force field model is trained on total energy and forces, with the inclusion of electrostatic energy. To evaluate the performance of our algorithm, we conducted tests on three benchmark systems, including a Ge slab with an O adatom system, a TiO2 crystalline system, and a Pd-O nanoparticle system. Our results demonstrate reasonably accurate predictions of partial charges and electrostatic interactions. This algorithm provides a self-consistent charge prediction strategy and possibilities for robust and reliable modeling of electrostatic interactions in machine-learning potentials.

Ion-ion association is lost by linearizing the Poisson-Boltzmann equation when deriving the Debye-Hückel equation.

In this work, we demonstrate how the ion association constant can be attributed to the difference between the full Poisson-Boltzmann equation and its linearized version in very dilute solutions. We follow a pragmatic approach first by deriving an analytical approximated solution to the Poisson-Boltzmann equation, then calculating its respective Helmholtz free energy and activity coefficient, and then finally comparing it to the contribution from the mass action law principle. The final result is the Ebeling association constant. We conclude that electrostatic ion-ion interaction models miss the ion association contribution naturally introduced in higher-order electrostatic theories. We also demonstrate how the negative deviations from the Debye-Hückel limiting law can be physically attributed to the ion association phenomenon.

PMC-IZ: A Simple Algorithm for the Electrostatics Calculation in Slab Geometric Molecular Dynamics Simulations.

Slab geometric systems are widely utilized in molecular simulations. However, an efficient, straightforward, and accurate method for calculating electrostatic interactions in these systems for molecular dynamics (MD) simulations is still needed. This review introduces a PME-like approach called PMC-IZ, specifically designed for slab geometric systems. Traditional approaches for long-range electrostatic interaction calculations in slab geometry typically involve Ewald summation, where the Gaussian charge density is summed within 3D unit cells and then integrated in the 2D periodic space. In the proposed approach here, the Poisson equation was solved for a single Gaussian charge density within 2Dl periodic space, followed by convolution within 3D unit cells using an effective potential as the convolution kernel for summation. The effective potential ensures that the solution within the region of interest adheres strictly to 2D periodic boundary conditions while inherently possessing 3D periodic boundary condition properties. The PMC-IZ method provides for such systems accurate treatment of electrostatic interactions, overcomes limitations associated with finite vacuum layers, and offers improved computational efficiency. We thus postulate that this method provides a valuable tool for studying electrostatic interactions in slab geometric system MD simulations. It has promising applications in various areas such as surface science, catalysis, and materials research, where accurate modeling of slab geometric electrostatic interactions is essential.

Repurposing Drugs for Inhibition against ALDH2 via a 2D/3D Ligand-Based Similarity Search and Molecular Simulation.

Aldehyde dehydrogenase-2 (ALDH2) is a crucial enzyme participating in intracellular aldehyde metabolism and is acknowledged as a potential therapeutic target for the treatment of alcohol use disorder and other addictive behaviors. Using previously reported ALDH2 inhibitors of Daidzin, CVT-10216, and CHEMBL114083 as reference molecules, here we perform a ligand-based virtual screening of world-approved drugs via 2D/3D similarity search methods, followed by the assessments of molecular docking, toxicity prediction, molecular simulation, and the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) analysis. The 2D molecular fingerprinting of ECFP4 and FCFP4 and 3D molecule-shape-based USRCAT methods show good performances in selecting compounds with a strong binding behavior with ALDH2. Three compounds of Zeaxanthin (q = 0), Troglitazone (q = 0), and Sequinavir (q = +1 e) are singled out as potential inhibitors; Zeaxanthin can only be hit via USRCAT. These drugs displayed a stronger binding strength compared to the reported potent inhibitor CVT-10216. Sarizotan (q = +1 e) and Netarsudil (q = 0/+1 e) displayed a strong binding strength with ALDH2 as well, whereas they displayed a shallow penetration into the substrate-binding tunnel of ALDH2 and could not fully occupy it. This likely left a space for substrate binding, and thus they were not ideal inhibitors. The MM-PBSA results indicate that the selected negatively charged compounds from the similarity search and Vina scoring are thermodynamically unfavorable, mainly due to electrostatic repulsion with the receptor (q = -6 e for ALDH2). The electrostatic attraction with positively charged compounds, however, yielded very strong binding results with ALDH2. These findings reveal a deficiency in the modeling of electrostatic interactions (in particular, between charged moieties) in the virtual screening via the 2D/3D similarity search and molecular docking with the Vina scoring system.

Asymmetry of the Electrostatic Environment as the Origin of the Symmetry Breaking Effect of the Nitrate Ion in Aqueous Solution.

Elucidating the mechanism of how vibrational modes are affected by intermolecular interactions is important for a better understanding of the nature of the former as probes of the latter. Here, such an analysis is carried out for the N-O stretching modes of the nitrate ion interacting with water, with an emphasis on the symmetry breaking effect. On the basis of theoretical calculations on the structural, vibrational, and electrostatic properties of molecular clusters and spectral simulations for an aqueous solution, a transparent view is demonstrated on the mechanism that modulations of spatially local electrostatic environment give rise to structural and spectroscopic symmetry breaking effect. The electrostatic interaction model constructed here is a seven-parameter model; the use of a single electrostatic parameter, such as the electric field on a single atomic site, is found to be insufficient for quantitative evaluation. It is also shown that the frequency modulations of the N-O stretching modes in aqueous solution occur on a time scale much shorter than 0.1 ps.

Impact of External Electronic Perturbations on Single-Walled Carbon Nanotube Electronic Structure: Scanning Tunneling Spectroscopy and Density Functional Theory

Understanding the local impact of environmental electronic perturbations on the local density of states (LDOS) of single-walled carbon nanotubes (CNTs) is critical for developing CNT-based devices. We present scanning tunneling microscopy and spectroscopy (STM/STS) investigations of CNTs adsorbed on both a metal, Au(111), and a dielectric, monolayer RbI on Au(111), serving as models for stronger and weaker electrostatic interactions, respectively. In both cases, STS revealed modulations in the CNT LDOS corresponding to features in the underlying material. We corroborate our STM/STS results with density functional theory calculations of the electronic structure of semiconducting CNTs in the presence and absence of an external dipole. DFT-calculated CNT LDOS qualitatively matched STM/STS results, providing key insight into the local impact external charges have on CNT electronic structure.

Role of the electrostatic interactions in the changes in the CN stretching frequency of benzonitrile interacting with hydrogen-bond donating molecules

An electrostatic interaction model of the vibrational frequency changes occurring upon intermolecular interactions is developed for the CN stretching mode of benzonitrile. The model encompasses both the cases of interaction with hydrogen-bonding solvent and uniform electric field. In the latter case, the model parameters are consistent with known vibrational properties of the mode. In the former case, the frequency changes are correlated to some intermolecular structural properties, and the good performance of the model indicates that those structural properties modulate the frequency through electrostatic interactions. On the basis of this, the spatially localized nature of the intermolecular interactions giving rise to the frequency variation observed in solutions is discussed.

Diffusion NMR-based comparison of electrostatic influences of DNA on various monovalent cations

Counterions are important constituents for the structure and function of nucleic acids. Using 7Li and 133Cs nuclear magnetic resonance (NMR) spectroscopy, we investigated how ionic radii affect the behavior of counterions around DNA through diffusion measurements of Li+ and Cs+ ions around a 15-bp DNA duplex. Together with our previous data on 23Na+ and 15NH4+ ions around the same DNA under the same conditions, we were able to compare the dynamics of four different monovalent ions around DNA. From the apparent diffusion coefficients at varied concentrations of DNA, we determined the diffusion coefficients of these cations inside and outside the ion atmosphere around DNA (Db and Df, respectively). We also analyzed ionic competition with K+ ions for the ion atmosphere and assessed the relative affinities of these cations for DNA. Interestingly, all cations (i.e., Li+, Na+, NH4+, and Cs+) analyzed by diffusion NMR spectroscopy exhibited nearly identical Db/Df ratios despite the differences in their ionic radii, relative affinities, and diffusion coefficients. These results, along with the theoretical relationship between diffusion and entropy, suggest that the entropy change due to the release of counterions from the ion atmosphere around DNA is also similar regardless of the monovalent ion types. These findings and the experimental diffusion data on the monovalent ions are useful for examination of computational models for electrostatic interactions or ion solvation.

HSMA: An O(N) electrostatics package implemented in LAMMPS

We implement two recently developed fast Coulomb solvers, HSMA3D (Zhao et al. (2018) [49]) and HSMA2D (Liang et al. (2020) [50]), into a new user package HSMA for the molecular dynamics simulation engine LAMMPS. The HSMA package is designed for efficient and accurate modeling of electrostatic interactions in 3D and 2D periodic systems with dielectric effects at O(N) cost. The implementation is hybrid MPI and OpenMP parallelized and compatible with existing LAMMPS functionalities. The vectorization technique following AVX512 instructions is adopted for acceleration. To establish the validity of our implementation, we have presented extensive comparisons to the widely used particle-particle particle-mesh (PPPM) algorithm in LAMMPS and other dielectric solvers. With the proper choice of algorithm parameters and parallelization setup, the package enables calculations of electrostatic interactions that is efficient especially for systems with dielectric mismatch. Program summaryProgram Title: HSMACPC Library link to program files:https://doi.org/10.17632/z39zyh573s.1Developer's repository link:https://github.com/LiangJiuyang/HSMA-Harmonic-surface-mapping-algorithm-in-LAMMPSLicensing provisions: GPLv3Programming language: C++Nature of problem: Evaluation of long-range electrostatic interactions for charged system with fully periodic condition or confined by planar dielectric interfaces.Solution method: We implement the Harmonic Surface Mapping algorithm (HSMA), which combines the image-charge method with the harmonic surface mapping and converts the contribution of infinite images into a finite number of surface charges on an auxiliary sphere, into simulation package LAMMPS. The HSMA package works for both fully periodic systems and partially periodic systems with planar dielectric interfaces, achieving truly linear O(N) complexity by employing fast multipole method. Our package can be applied to general all-atom simulations and a broad range of charged complex fluids under dielectric confinement.Additional comments including restrictions and unusual features: Hybrid MPI plus OpenMP parallelization is used in HSMA package for high-performance computing. We provide vector optimization by using the AVX512 instructions and Intel MKL library for further acceleration. The Intel Parallel Studio is required for these techniques.

Topological Phase Transition of Photonic Crystals Based on Electrostatic Interaction Model

Topological Phase Transition of Photonic Crystals Based on Electrostatic Interaction Model

On the Role of Long-Range Electrostatics in Machine-Learned Interatomic Potentials for Complex Battery Materials

Modeling complex energy materials such as solid-state electrolytes (SSEs) realistically at the atomistic level strains the capabilities of state-of-the-art theoretical approaches. On one hand, the system sizes and simulation time scales required are prohibitive for first-principles methods such as the density functional theory. On the other hand, parameterizations for empirical potentials are often not available, and these potentials may ultimately lack the desired predictive accuracy. Fortunately, modern machine learning (ML) potentials are increasingly able to bridge this gap, promising first-principles accuracy at a much reduced computational cost. However, the local nature of these ML potentials typically means that long-range contributions arising, for example, from electrostatic interactions are neglected. Clearly, such interactions can be large in polar materials such as electrolytes, however. Herein, we investigate the effect that the locality assumption of ML potentials has on lithium mobility and defect formation energies in the SSE Li7P3S11. We find that neglecting long-range electrostatics is unproblematic for the description of lithium transport in the isotropic bulk. In contrast, (field-dependent) defect formation energies are only adequately captured by a hybrid potential combining ML and a physical model of electrostatic interactions. Broader implications for ML-based modeling of energy materials are discussed.

Numerical analysis of frictional charging and electrostatic interaction of particles

AbstractTriboelectrification due to frictional contacts between particles and surfaces is prevalent in many powder handling processes. Aiming to explore the friction‐induced electrostatic charging behavior, a discrete element method (DEM) is developed for the first time in the current article, in which a frictional charging model and electrostatic interaction models are implemented. The charge accumulation on both the particles and the surface in a rotational container is then analyzed numerically and experimentally to evaluate the developed DEM. The numerical results for the frictional electrification between insulant particles and an insulant wall agree well with the experimental measurement. It is also shown that both the net charge on the particles and the degree of the particle dispersion are a function of the charging time. Moreover, it is revealed that the friction‐induced particle charge enhances particle dispersion, and increases the granular temperature due to the electrostatic interactions.

Solving nonlinear reaction–diffusion problem in electrostatic interaction with reaction-generated pH change on the kinetics of immobilized enzyme systems using Taylor series method

A mathematical model of electrostatic interaction with reaction-generated pH change on the kinetics of immobilized enzyme is discussed. The model involves the coupled system of non-linear reaction–diffusion equations of substrate and hydrogen ion. The non-linear term in this model is related to the Michaelis–Menten reaction of the substrate and non-Michaelis–Menten kinetics of hydrogen ion. The approximate analytical expression of concentration of substrate and hydrogen ion has been derived by solving the non-linear reactions using Taylor’s series method. Reaction rate and effectiveness factor are also reported. A comparison between the analytical approximation and numerical solution is also presented. The effects of external mass transfer coefficient and the electrostatic potential on the overall reaction rate were also discussed.

Crystal Field Effects on Atomic and Functional-Group Distributed Polarizabilities of Molecular Materials.

To rationally design new molecular materials with desirable linear optical properties, such as refractive index or birefringence, we investigated how atomic and functional-group polarizability tensors of prototypical molecules respond to crystal field effects. By building finite aggregates of urea, succinic acid, p-nitroaniline, 4-mercaptopyridine, or methylbenzoate, and by partitioning the cluster electronic density using quantum theory of atoms in molecules, we could extract atoms and functional groups from the aggregates and estimate their polarizability enhancements with respect to values calculated for molecules in isolation. The isotropic polarizability and its anisotropy for the molecular building blocks are used to understand the functional-group sources of optical properties in these model systems, which could help the synthetic chemist to fabricate efficient materials. This analysis is complemented by benchmarking density functionals for atomic distributed polarizabilities in gas phase, by comparing the results with refractive-index calculations under periodic boundary conditions, and by estimating functional-group optical properties from a classical electrostatic atom-dipole interaction model.

On the voltage-controlled assembly of nanoparticle arrays at electrochemical solid/liquid interfaces

Research in the field of nanoplasmonic metamaterials is moving towards more and more interesting and, potentially useful, applications. In this paper we focus on a class of such metamaterials formed by voltage controlled self-assembly of metallic nanoparticale at electrochemical solid |liquid interfaces. We perform a simplified, comprehensive analysis of the stability of a nanoparticle arrays under different conditions and assembly. From the Poisson-Boltzmann model of electrostatic interactions between a metallic nanoparticle and the electrode and between the nanoparticles at the electrode, as well as the Hamaker-Lifshitz theory of the corresponding van der Waals interactions, we reach some conclusions regarding the possibility to build arrays of charged nanoparticles on electrodes and disassemble them, subject to variation of applied voltage. Since systems of this type have been shown, recently, to provide nontrivial electrotuneable optical response, such analysis is crucial for answering the question whether the scenarios of electrochemical plasmonics are feasible.

Dielectric characterization of erythrocytes by electrostatic force microscopy

The method of determination of the dielectric constant of individual erythrocytes, based on a quantitative analysis of the profiles of their images obtained by electrostatic force microscopy, is presented. A model of electrostatic interaction between the atomic force microscope probe and the biological cell is proposed. The obtained values of the permittivity of individual erythrocytes agree well with known literature data.