Unification of Ewald and shifted force methods to calculate Coulomb interactions in molecular simulations.

The article focuses on evaluating and improving methods for calculating Coulomb interactions in molecular dynamics (MD) simulations, particularly comparing the traditional Ewald method and its variants with the shifted force (SF) cut-off approach. Three new Ewald series are derived without relying on predefined charge spreading functions, including formulations using shifted potential (SP) and shifted force (SF) real space terms; however, the SF-based Ewald series is found not to converge, explaining the erratic errors observed in SF simulations. Molecular simulations of a high-pressure ionic melt (cesium iodide) and liquid water demonstrate that the recently developed α′ variant of the Ewald method offers significantly better accuracy and computational efficiency than SF, especially in reproducing Coulomb energies, forces, and pressure fluctuations, while also conserving the shadow Hamiltonian for improved long-term stability. The α′ and Extended Shell Gaussian Ewald (GEwES) methods allow reduced reciprocal space computations and smaller real space cutoffs, resulting in faster simulations with accuracy close to exact Ewald calculations, whereas SF requires larger cutoffs and exhibits poorer pressure correlations and energy conservation. The study highlights the importance of validating Coulomb interaction methods against exact treatments and suggests that α′ and GEwES provide superior alternatives to SF for simulating charged molecular systems.