The optimal P3M algorithm for computing electrostatic energies in periodic systems

Abstract

We optimize Hockney and Eastwood's Particle-Particle Particle-Mesh (P3M) algorithm to achieve maximal accuracy in the electrostatic energies (instead of forces) in 3D periodic charged systems. To this end we construct an optimal influence function that minimizes the RMS errors in the energies. As a by-product we derive a new real-space cut-off correction term, give a transparent derivation of the systematic errors in terms of Madelung energies, and provide an accurate analytical estimate for the RMS error of the energies. This error estimate is a useful indicator of the accuracy of the computed energies, and allows an easy and precise determination of the optimal values of the various parameters in the algorithm (Ewald splitting parameter, mesh size and charge assignment order).

Percolation-induced conductor-insulator transition in a system of metal spheres in a dielectric fluid

“…In recent years, there are significant developments in the simulation techniques for the soft-matter systems [23][24][25]. However, for the calculations on the electrostatics of the systems composed of particles, the most efficient methods are based upon the particle-particle-particle-mesh algorithm [26,27], which is not enough in treating the system with the size we used in this paper. To obtain the electrostatics, we generally solve Maxwell equations with a complex permittivity, which combines the information of permittivity and conductance together.…”

Long ranged interactions in computer simulations and for quasi-2D systems

“…In Particle-Particle Particle Mesh Ewald method (PPPM or P3M) [335,253,254,268,155] (and also Ref. [336] for a new development and parallel implementation), the Fourier transform of pth-order charge assignment function is chosen aŝ…”

Removal of spurious self-interactions in particle–mesh methods

“…A correction of this kind has been introduced in Ref. [16] to remove, on average, the bias of the P3M energies that is caused by the approximate (mesh computed) self-interactions. Correcting exactly these self-interactions at the level of each particle will improve the accuracy of the computed energies beyond the average correction of Ref.…”

“…Correcting exactly these self-interactions at the level of each particle will improve the accuracy of the computed energies beyond the average correction of Ref. [16].…”