Multiple Staggered Mesh Ewald: Boosting the Accuracy of the Smooth Particle Mesh Ewald Method

TL;DR

This paper introduces the multiple staggered mesh Ewald (MSME) method, which enhances the accuracy of electrostatic calculations in molecular simulations by averaging forces on staggered meshes, reducing mesh points needed.

Contribution

The paper proposes MSME, a novel approach that improves SPME accuracy through mesh averaging, requiring fewer mesh points or higher interpolation order, with theoretical and numerical validation.

Findings

MSME achieves accuracy comparable to SPME with fewer mesh points.

MSME's accuracy matches SPME with doubled interpolation order in certain parameters.

Numerical tests confirm MSME's effectiveness on charge systems and water models.

Abstract

The smooth particle mesh Ewald (SPME) method is the standard method for computing the electrostatic interactions in the molecular simulations. In this work, the multiple staggered mesh Ewald (MSME) method is proposed to boost the accuracy of the SPME method. Unlike the SPME that achieves higher accuracy by refining the mesh, the MSME improves the accuracy by averaging the standard SPME forces computed on, e.g. $M$, staggered meshes. We prove, from theoretical perspective, that the MSME is as accurate as the SPME, but uses $M^2$ times less mesh points in a certain parameter range. In the complementary parameter range, the MSME is as accurate as the SPME with twice of the interpolation order. The theoretical conclusions are numerically validated both by a uniform and uncorrelated charge system, and by a three-point-charge water system that is widely used as solvent for the bio-macromolecules.