Ewald summation

<p>Ewald summation, named after <a href="/facts/Paul_Peter_Ewald/2IKqEFNe">Paul Peter Ewald</a>, is a method for computing long-range interactions (e.g. <a href="/facts/Electrostatic_interaction/bxkuW6s4">electrostatic interactions</a>) in periodic systems. It was first developed as the method for calculating the electrostatic energies of <a href="/facts/Ionic_crystal/6YbBy9DV">ionic crystals</a>, and is now commonly used for calculating long-range interactions in <a href="/facts/Computational_chemistry/KyuCgRV3">computational chemistry</a>. Ewald summation is a special case of the <a href="/facts/Poisson_summation_formula/CDM4uRPs">Poisson summation formula</a>, replacing the summation of interaction energies in real space with an equivalent summation in <a href="/facts/Fourier_space/pyTVrUSq">Fourier space</a>. In this method, the long-range interaction is divided into two parts: a short-range contribution, and a long-range contribution which does not have a <a href="/facts/Singularity_(mathematics)/Y5sMQY4I">singularity</a>. The short-range contribution is calculated in real space, whereas the long-range contribution is calculated using a <a href="/facts/Fourier_transform/XXhKJtc8">Fourier transform</a>. The advantage of this method is the rapid <a href="/facts/Convergence_(mathematics)/DTok170z">convergence</a> of the energy compared with that of a direct summation. This means that the method has high accuracy and reasonable speed when computing long-range interactions, and it is thus the de facto standard method for calculating long-range interactions in periodic systems. The method requires charge neutrality of the molecular system to accurately calculate the total Coulombic interaction. A study of the truncation errors introduced in the energy and force calculations of disordered point-charge systems is provided by Kolafa and Perram.
</p>

Ewald summation open-in-new

Ewald summation