Ewald summation, named after Paul Peter Ewald, is a method for computing long-range interactions (e.g. electrostatic interactions) in periodic systems. It was first developed as the method for calculating the electrostatic energies of ionic crystals, and is now commonly used for calculating long-range interactions in computational chemistry. Ewald summation is a special case of the Poisson summation formula, replacing the summation of interaction energies in real space with an equivalent summation in Fourier space. 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 singularity. The short-range contribution is calculated in real space, whereas the long-range contribution is calculated using a Fourier transform. The advantage of this method is the rapid convergence 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.[1]
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Kolafa, Jiri; Perram, John W. (September 1992). "Cutoff Errors in the Ewald Summation Formulae for Point Charge Systems". Molecular Simulation. 9 (5): 351–368. doi:10.1080/08927029208049126.
Ewaldsummation, named after Paul Peter Ewald, is a method for computing long-range interactions (e.g. electrostatic interactions) in periodic systems...
mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values...
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Crystallography) Peter Paul Ewald On the Foundations of Crystal Optics (Air Force Cambridge Research Laboratories, 1970) EwaldsummationEwald's sphere Multiple scattering...
Particle–Particle–Particle–Mesh (P3M) is a Fourier-based Ewaldsummation method to calculate potentials in N-body simulations. The potential could be...
field method is an alternative to the popular technique of Ewaldsummation. Today, Ewaldsummation is the usual technique of choice, but for many quantities...
infinity. PBCs can be used in conjunction with Ewaldsummation methods (e.g., the particle mesh Ewald method) to calculate electrostatic forces in the...
or the short-range part of the electrostatic interaction when using Ewaldsummation. Cell lists work by subdividing the simulation domain into cells with...
periodic electrostatic conditions (Ewaldsummation), a modified version was published later optimized by using the Ewald method for estimating the Coulomb...
of the code and revision control for greater maintainability, PME Ewaldsummations, tools for NMR refinement, and many others. Currently, AMBER is maintained...
the cutoff radius if sufficient smoothing is not used. Particle mesh Ewaldsummation is one solution for this effect, but introduces artifacts of its own...
efficiency of the fast multipole method is generally similar to that of Ewaldsummation, but is superior if the particles are clustered, i.e. the system has...
Potentials with an infinite range can be summed up efficiently by Ewaldsummation and its further developments. The forces acting between atoms can be...
Fourier transforms are used throughout the CASTEP code, as is the Ewaldsummation method for Coulombic energies. Along with plane waves and iterative...
{\frac {N(N-1)}{2}}} interactions. Advanced algorithms, such as the Ewaldsummation or Fast Multipole Method, reduce this to O ( N log N ) {\displaystyle...
stellar systems. It is based on the Barnes–Hut algorithm and uses Ewaldsummation for periodic forces. ChaNGa makes use of the Charm++ parallel programming...
of MoM. The fast multipole method (FMM) is an alternative to MoM or Ewaldsummation. It is an accurate simulation technique and requires less memory and...
systems. To determine the net forces acting on particles, the Ewald or Lekner summation methods are generally employed. One alternative and usually computationally...
Algorithms are included for NVE, NVT, NPT, anisotropic NPT ensembles, and Ewaldsummation to treat electrostatic interactions. The code was written in a mix...
L. (2004). "A modified TIP3P water potential for simulation with Ewaldsummation". The Journal of Chemical Physics. 121 (20): 10096–10103. Bibcode:2004JChPh...
faster than a full explicit solvent simulation with the particle mesh Ewaldsummation (PME) method of electrostatic calculation. There are a range of hybrid...
addition to the PM calculation. P3M Particle mesh method Particle mesh Ewald method Madelung constant Poisson summation formula Paul Peter Ewald v t e...
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