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To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of…

Computational Physics · Physics 2021-02-24 William Robert Saunders , James Grant , Eike Hermann Müller

Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. We present an analysis of the errors arising from truncating the infinite real- and Fourier-space lattice sums in…

chem-ph · Physics 2016-08-31 Gerhard Hummer

Dielectrically confined Coulomb systems are widely employed in molecular dynamics (MD) simulations. Despite extensive efforts in developing efficient and accurate algorithms for these systems, rigorous and accurate error estimates, which…

Numerical Analysis · Mathematics 2025-03-25 Xuanzhao Gao , Qi Zhou , Zecheng Gan , Jiuyang Liang

Particle Mesh Ewald (PME) methods accelerated through Fast Fourier Transforms (FFTs) for their reciprocal part are widely used to solve N -body problems over periodic structures with Laplace-like kernels. The FFT dependence of classical PME…

Numerical Analysis · Mathematics 2026-01-28 Igor Chollet

This paper compares the Wolf method to the shifted forces (SF) method for efficient computer simulation of isotropic systems interacting via Coulomb forces, taking results from the Ewald summation method as representing the true behavior.…

Mesoscale and Nanoscale Physics · Physics 2012-12-19 Jesper S. Hansen , Thomas B. Schrøder , Jeppe C. Dyre

We present a new approach to efficiently simulate electrolytes confined between infinite charged walls using a 3d Ewald summation method. The optimal performance is achieved by separating the electrostatic potential produced by the charged…

Soft Condensed Matter · Physics 2018-01-18 Alexandre P. dos Santos , Matheus Girotto , Yan Levin

A new method for Ewald summation in planar/slablike geometry, i.e. systems where periodicity applies in two dimensions and the last dimension is "free" (2P), is presented. We employ a spectral representation in terms of both Fourier series…

Computational Physics · Physics 2015-05-30 Dag Lindbo , Anna-Karin Tornberg

Classical Ewald methods for Coulomb and Stokes interactions rely on ``kernel-splitting," using decompositions based on Gaussians to divide the resulting potential into a near field and a far field component. Here, we show that a more…

Numerical Analysis · Mathematics 2025-09-29 Ludvig af Klinteberg , Leslie Greengard , Shidong Jiang , Anna-Karin Tornberg

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with…

Machine Learning · Computer Science 2023-06-07 Arthur Kosmala , Johannes Gasteiger , Nicholas Gao , Stephan Günnemann

Massively-parallel molecular dynamics simulation is applied to systems containing electrolytes, vapour-liquid interfaces, and biomolecules in contact with water-oil interfaces. Novel molecular models of alkali halide salts are presented and…

The evaluation of Coulomb forces is a difficult task. The summations that are involved converge only conditionally and care has to be taken in selecting the appropriate procedure to define the limits. The Ewald method is a standard method…

mtrl-th · Physics 2008-02-03 Michael J. Love , Henri J. F. Jansen

The constant potential molecular dynamics simulation method proposed by Siepmann and Sprik and reformulated later by Reed (SR-CPM) has been widely employed to investigate the metallic electrolyte/electrode interfaces, especially for…

Chemical Physics · Physics 2022-05-04 Haoyu Li , Peiyao Wang , Jefferson Zhe Liu , Gengping Jiang

This paper introduces a random-batch molecular dynamics (RBMD) package for fast simulations of particle systems at the nano/micro scale. Different from existing packages, the RBMD uses random batch methods for nonbonded interactions of…

Computational Physics · Physics 2025-11-11 Weihang Gao , Teng Zhao , Yongfa Guo , Jiuyang Liang , Huan Liu , Maoying Luo , Zedong Luo , Wei Qin , Yichao Wang , Qi Zhou , Shi Jin , Zhenli Xu

Neural network-based molecular dynamics (NNMD) simulations incorporating long-range electrostatic interactions have significantly extended the applicability to heterogeneous and ionic systems, enabling effective modeling critical physical…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-04-23 Jianxiong Li , Beining Zhang , Mingzhen Li , Siyu Hu , Jinzhe Zeng , Lijun Liu , Guojun Yuan , Zhan Wang , Guangming Tan , Weile Jia

We present an efficient algorithm for the all-electron periodic Coulomb matrix based on the Ewald summation combined with the Fourier-transformed Coulomb method. The short-range contributions involving compact densities are evaluated in…

Chemical Physics · Physics 2025-09-23 Hieu Q. Dinh , Adam Rettig , Xintian Feng , Joonho Lee

Molecular Dynamics (MD) codes predict the fundamental properties of matter by following the trajectories of a collection of interacting model particles. To exploit diverse modern manycore hardware, efficient codes must use all available…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-08-04 William R. Saunders , James Grant , Eike H. Müller

Machine learning potentials have emerged as a means to enhance the accuracy of biomolecular simulations. However, their application is constrained by the significant computational cost arising from the vast number of parameters compared to…

The random batch Ewald (RBE) is an efficient and accurate method for molecular dynamics (MD) simulations of physical systems at the nano-/micro- scale. The method shows great potential to solve the computational bottleneck of long-range…

Computational Physics · Physics 2022-05-31 Jiuyang Liang , Zhenli Xu , Yue Zhao

A proper treatment of electrostatic interactions is crucial for the accurate calculation of forces in computer simulations. Electrostatic interactions are typically modeled using Ewald based methods, which have become one of the…

Soft Condensed Matter · Physics 2016-09-21 K. A. Terrón-Mejía , R. López-Rendón , A. Gama Goicochea

Molecular dynamics (MD) simulation is a widely used technique to simulate molecular systems, most commonly at the all-atom resolution where equations of motion are integrated with timesteps on the order of femtoseconds…