The optimal P3M algorithm for computing electrostatic energies in periodic systems

Details The optimal P3M algorithm for computing electrostatic energies in periodic systems The optimal P3M algorithm for computing electrostatic energies in periodic systems

2007-08-06

arxiv.org/abs/0708.0728v1

J. Chem. Phys. 128, 034109 (2008)

Physics

Computational Physics

31 pages, 3 figures

Scientific paper

10.1063/1.2816570

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).

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