Particle-mesh Ewald,

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... 

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... 

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. 

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. 

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... 

One of the most efficient algorithms known for evaluating the Ewald sum is the Particle-mesh Ewald (PME) method of Darden et al. [8, 9]. The use of Ewald s trick of splitting the Coulomb sum into real space and Fourier space parts yields two distinct computational problems. The relative amount of work performed in real space vs Fourier space can be adjusted within certain limits via a free parameter in the method, but one is still left with two distinct calculations. PME performs the real-space calculation in the conventional manner, evaluating the complementary error function within a cutoff... 

A. Toukmaji and D. Paul and J. A. Board, Jr., Distributed Particle-Mesh Ewald A Parallel Ewald Summation Method, Proceedings, International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA 96), CSREA Press (1996), pp. 33-43. 

In periodic boimdary conditions, one possible way to avoid truncation of electrostatic interaction is to apply the so-called Particle Mesh Ewald (PME) method, which follows the Ewald summation method of calculating the electrostatic energy for a number of charges [27]. It was first devised by Ewald in 1921 to study the energetics of ionic crystals [28]. PME has been widely used for highly polar or charged systems. York and Darden applied the PME method already in 1994 to simulate a crystal of the bovine pancreatic trypsin inhibitor (BPTI) by molecular dynamics [29]. 

Cheatham T E III, J L Miller, T Fox, T A Darden and P A Kollman 1995. Molecular Dynamics Simulations on Solvated Biomolecular Systems The Particle Mesh Ewald Method Leads to Stable Trajectories of DNA, RNA and Proteins. Journal of the American Chemical Society 117 4193-4194. 

Darden T A, L Perera, L Li and L Pedersen 1999. New Tricks for Modelers from the Crystallography Toolkit The Particle Mesh Ewald Algorithm and Its Use in Nucleic Acid Simulations. Structure with Folding and Design 7 R55-R60. 

Desemo M and C Holm 1998a. How to Mesh Up Ewald Sums. I. A Theoretical and Numerical Comparison of Various Particle Mesh Routines. Journal of Chemical Physics 109 7678-7693. 

Luty B A, M E David, I G Tironi and W F van Gunsteren 1994. A Comparison of Particle-Particle, Particle-Mesh and Ewald Methods for Calculating Electrostatics Interactions in Periodic Molecular Systems. Molecular Simulation 14 11-20. 

In the case of the reciprocal sum, two methods have been implemented, smooth particle mesh Ewald (SPME) [65] and fast Fourier Poisson (FFP) [66], SPME is based on the realization that the complex exponential in the structure factors can be approximated by a well behaved function with continuous derivatives. For example, in the case of Hermite charge distributions, the structure factor can be approximated by... 

Toukmaji A, Sagui C, Board J, Darden T (2000) Efficient particle-mesh Ewald based approach to fixed and induced dipolar interactions. J Chem Phys 113(24) 10913—10927... 

Darden T, Perera L, Li LP, Pedersen L (1999) New tricks for modelers from the crystallography toolkit the particle mesh Ewald algorithm and its use in nucleic acid simulations. Struct Fold Des 7(3) R55-R60... 

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