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

The smooth particle mesh Ewald (SPME) method is the standard method for computing the electrostatic interactions in the molecular simulations. In this work, we develop the multiple staggered mesh Ewald (MSME) method, which averages the SPME forces computed on, for example, M, staggered meshes. We prove, from a theoretical perspective, that the MSME is as accurate as the SPME, but uses M² times less mesh points in a certain parameter range. In the complementary parameter range, the MSME is as accurate as the SPME with twice 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 biomacromolecules.