Particle Mesh Ewald algorithm

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. 

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... 

Barash, D., Yang, L.J., Qian, X.L., SchUck, T. Inherent speedup limitations in multiple time step/particle mesh Ewald algorithms, J. Comput. Chem. 2003,24,77-88. 

Speedup Limitations in Multiple Timestep Particle Mesh Ewald Algorithms. 

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... 

The limit E exists and has as its value that of the Ewald method minus the dipole term [16]. Starting from this convergence factor approach, Strebel and Sperb constructed a method of computational order 0(A / ) or, with a more clever algorithm, (P(AllogAl), MMM [15]. Unlike the particle mesh Ewald methods, no mesh is introduced, so that no interpolation errors occur, and it is comparatively easy to find error estimates for the method. Consequently, this method allows much higher precisions compared to P M or (S)PME. 

A. C. Simmonett, F. C. Pickard IV, H. F. Schaefer III, B. R. Brooks, An efficient algorithm for multipole energies and derivatives based on spherical harmonics and extensions to particle mesh Ewald. /. Chem. Phys., 2014.140 184101. 

An alternative to truncation of any kind is the use of Ewald Sums, as originally introduced to calculate the lattice energy of ionic crystals. A fast algorithm, "Particle Mesh Ewald (PME)" (23), has recently been devised which makes this approach viable in full-scale MD on macromolecules in solvent. The initial round of PME simulations on DNA demonstrated a higher degree of stability and less deviation from the starting structure (24, 25). The accuracy of the... 

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