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We optimize Hockney and Eastwood's Particle-Particle Particle-Mesh (P3M)algorithm to achieve maximal accuracy in the electrostatic energies (instead offorces) in 3D periodic charged systems. To this end we construct an optimalinfluence function that minimizes the RMS errors in the energies. As aby-product we derive a new real-space cut-off correction term, give atransparent 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 computedenergies, and allows an easy and precise determination of the optimal values ofthe various parameters in the algorithm (Ewald splitting parameter, mesh sizeand charge assignment order).

The optimal P3M algorithm for computing electrostatic energies in periodic systems