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Ewald

P. P. Ewald and H. Juretschke, Structure and Properties of Solid Surfaces, University of Chicago Press, Chicago, 1953. [Pg.287]

Figure Bl.8.3. Ewald s reciprocal lattice construction for the solution of the Bragg equation. If Sj-s. is a vector of the reciprocal lattice, Bragg s law is satisfied for the corresponding planes. This occurs if a reciprocal lattice point lies on the surface of a sphere with radius 1/X whose centre is at -s.. Figure Bl.8.3. Ewald s reciprocal lattice construction for the solution of the Bragg equation. If Sj-s. is a vector of the reciprocal lattice, Bragg s law is satisfied for the corresponding planes. This occurs if a reciprocal lattice point lies on the surface of a sphere with radius 1/X whose centre is at -s..
When carried out properly, the results of the reaction field method and the Ewald sum are consistent [67]. Recently, the reaction field method has been reconnnended on grounds of elTiciency and ease of progrannning [68, 69]. The... [Pg.2255]

Gray C G, Sainger Y S, Joslin C G, Cummings P T and Goldman S 1986 Computer simulation of dipolar fluids. Dependence of the dielectric constant on system size a comparative study of Ewald sum and reaction field approaches J. Chem. Phys. 85 1502-4... [Pg.2282]

Gil-Villegas A, McGrother S C and Jackson G 1997 Reaction-field and Ewald summation methods in Monte Carlo simulations of dipolar liquid crystals Mol. Phys. 92 723-34... [Pg.2282]

Darden T, York D and Pedersen L 1993 Particle mesh Ewald—an N.log(N) method for Ewald sums in large systems J. Chem. Phys. 98 10089-92... [Pg.2282]

Essmann U, Perera L, Berkowitz M L, Darden T, Lee H and Pedersen L G 1995 A smooth particle mesh Ewald method J. Chem. Phys. 103 8577-93... [Pg.2282]

Smith W 1992 A replicated data molecular dynamics strategy for the parallel Ewald sum Comput. Phys. Commun. 67 392-406... [Pg.2289]

But the methods have not really changed. The Verlet algorithm to solve Newton s equations, introduced by Verlet in 1967 [7], and it s variants are still the most popular algorithms today, possibly because they are time-reversible and symplectic, but surely because they are simple. The force field description was then, and still is, a combination of Lennard-Jones and Coulombic terms, with (mostly) harmonic bonds and periodic dihedrals. Modern extensions have added many more parameters but only modestly more reliability. The now almost universal use of constraints for bonds (and sometimes bond angles) was already introduced in 1977 [8]. That polarisability would be necessary was realized then [9], but it is still not routinely implemented today. Long-range interactions are still troublesome, but the methods that now become popular date back to Ewald in 1921 [10] and Hockney and Eastwood in 1981 [11]. [Pg.4]

Separation of Short- and Long-Range Ewald and PPPM Methods If we split the total Coulomb interaction in a short- and a long-range contribution, chosen to be smooth functions of the distance, the two... [Pg.11]

Luty, B.A., Davis, M.E., Tironi, I.G., Van Gunsteren, W.F. A comparison of particle-particle particle-mesh and Ewald methods for calculating interactions in periodic molecular systems. Mol. Simul. 14 (1994) 11-20. [Pg.32]

Belhadj,M., Alper, H.A., Levy, R.M. Molecular dynamics simulations of wa ter with Ewald summation for the long-range electrostatic interactions. Chem. Phys. Lett. 179 (1991) 13-20. [Pg.32]

U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen. The smooth particle mesh ewald method. J. Chem. Phys., 103 8577, 1995. Brock A. Luty, Ilario G. Tironi, and Wilfried F. van Gunsteren. Lattice-sum methods for calculating electrostatic interactions in molecular simulations. J. Chem. Phys., 103 3014-3021, 1995. [Pg.96]

There are three different algorithms for the calculation of the electrostatic forces in systems with periodic boundary conditions (a) the (optimized) Ewald method, which scales like (b) the Particle Mesh... [Pg.310]

Ewald and Multipole Methods for Periodic JV-Body Problems ... [Pg.459]

Ewald summation was invented in 1921 [7] to permit the efl5.cient computation of lattice sums arising in solid state physics. PBCs applied to the unit cell of a crystal yield an infinite crystal of the appropriate. symmetry performing... [Pg.462]

Ewald s formalism reduces the infinite lattice sum to a serial complexity of in the number of particles n, which has been reduced to n logn in more recent formulations. A review of variants on Ewald summation methods which includes a more complete derivation of the basic method is in [3]. [Pg.464]


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Diffraction Ewald sphere

Dynamical matrix by Ewald-Fuchs method

Electrostatics Ewald

Energy contributions in Ewald formulation

Ewald Sphere and Reciprocal Space

Ewald algorithm

Ewald approach

Ewald approximation

Ewald circle

Ewald conducting boundary conditions

Ewald construction

Ewald dimensions

Ewald energy calculation

Ewald gradient

Ewald image potential

Ewald lattice sums

Ewald method

Ewald parameter

Ewald particle mesh

Ewald potential

Ewald procedure

Ewald procedure potential

Ewald sphere

Ewald sphere construction

Ewald sphere construction in reciprocal space

Ewald sum

Ewald sum methods

Ewald summation

Ewald summation Coulomb interaction

Ewald summation computer time

Ewald summation dipole interaction

Ewald summation extended system

Ewald summation for confined fluids

Ewald summation method

Ewald summation parameters

Ewald summation rigorous

Ewald summation schemes

Ewald summation slab geometry

Ewald summation slab-adapted

Ewald summation techniques

Ewald summation three-dimensional

Ewald summation-based methods

Ewald term

Ewald theory

Ewald, Paul

Ewald, Paul Peter

Ewald, Peter

Ewalds Sphere

Ewald’s method

Ewald’s sphere

Generalized Ewald Method

Generalized Ewald-Oseen Extinction Theorem

Molecular dynamics Ewald summation

Particle Mesh Ewald algorithm

Particle Mesh Ewald method

Particle mesh Ewald electrostatics

Particle mesh Ewald simulation

Particle-mesh Ewald approach

Particle-mesh Ewald summation

Reciprocal lattice and Ewalds sphere

Reliability of the slab-adapted Ewald method

Smooth particle mesh Ewald

Smoothed particle mesh Ewald

The Ewald Construction

The Ewald X-Rays Diffraction Rationalization

The Ewald method

The Ewald sphere

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