P3MaZe: a Mass-Zero Constrained-Dynamics Formulation of Particle–Mesh Electrostatics

Abstract 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). Values of the potential, 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. We further show that, for the linear, time-independent Poisson operator considered here, the constrained correction problem is algebraically equivalent to a direct Poisson solve initialized by a chronological extrapolation of the mesh potential, a connection not previously established for MaZe-based approaches. This result identifies the precise mechanism through which acceleration of the iterative long-range solve is achieved, and we exploit it systematically through higher-order predictors to further improve convergence, while retaining the expected linear scaling with system size. Because the underlying extrapolation is independent of the constrained-dynamics formalism, it can, of course, also be used directly to accelerate conventional iterative real-space Poisson solvers.