An efficient real space method is derived for the evaluation of the Madelungs potential of ionic crystals. The proposed method is an extension of the Evjens method. It takes advantage of a general analysis for the potential convergence in real space. Indeed, we show that the series convergence is exponential as a function of the number of annulled multipolar momenta in the unit cell. The method proposed in this work reaches such an exponential convergence rate. Its efficiency is comparable to the Ewalds method, however unlike the latter, it uses only simple algebraic functions.
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