P3MaZe: a Mass-Zero constrained-dynamics formulation of particle–mesh electrostatics

We introduce P3MaZe, a real-space particle–mesh electrostatic method that combines the standard short-range/long-range decomposition of Particle-Particle Particle-Mesh (P3M) electrostatics with the Mass-Zero constrained dynamics (MaZe) framework. In this formulation, the smooth long-range electrostatic potential is represented on a mesh as a zero-inertia auxiliary field, while the discretized Poisson equation is enforced as a holonomic constraint during molecular dynamics. By retaining the standard P3M decomposition, P3MaZe preserves the systematic accuracy controls associated with the real-space cutoff, the Ewald splitting, the mesh spacing, and the charge assignment procedure, while replacing the conventional multigrid Poisson solver by a constrained correction problem. The method is validated for molten NaCl and simple point-charge flexible water (SPC/Fw). Structural, translational, collective, and rotational dynamical observables are in quantitative agreement with those obtained with established electrostatic methods, including real-space P3M, and Ewald summation. The constrained formulation consistently requires fewer multigrid iterations than the corresponding real-space P3M solver while retaining the expected linear scaling with system size. These results establish P3MaZe as a promising new direction for scalable real-space electrostatics in large-scale molecular simulations.