Smoothed particle mesh Ewald

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... 

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. 

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... 

Harvey, M.J., De Fabritiis, G. An implementation of the smooth particle mesh Ewald method on GPU hardware. J. Chem. Theory Comput. 2009, 5, 2371-7. 

Essmann, U., et al., A smooth particle mesh Ewald method. Journal of Chemical Physics, 1995,103(19) 8577-8593. 

Phys., 103, 8577 (1995). A Smooth Particle Mesh Ewald Method. 

Let us briefly summarize the numerical experiments of [220] using the SIN(R) method to simulate a system of 512 flexible water molecules using a fuUy flexible molecular model [294] and the smooth particle-mesh Ewald method (SPME) [123] (see Appendix A) to compute electrostatic forces. Initial simulations were conducted without a fast-slow force decomposition to demonstrate the effectiveness of the method as a thermostatting scheme. This technique was shown to allow accurate computation of the OH, HH and OO radial distribution functions when suitably small timesteps were used. 

Hiinenberger PH, van Gunsteren WF (1998) Alternative schemes for the inclusion of a reaction field correction into molecular dynamics simulations influence on the simulated energetic, structural, and dielectric properties of liquid water. J Chem Phys 108 6117-6134 89. Essmann U, Perera L, Berkowitz M, Darden T, Lee H, Pedersen L (1995) A smooth particle mesh Ewald method. J Chem Phys 103 8577-8593... 

The original literature on particle mesh routines is usually not easy to digest for the nonspedaHst. It is obscured by the fact that various authors approach the problem from different directions and use different notations. There exist three mesh implementations of the Ewald smn—similar in spirit but different in detail. The oldest is the original particle-particle-particle mesh (P M) method of Hockney and Eastwood [40], and then there are two variants, namely, the particle mesh Ewald (PME) method of Darden et aL [41] and an extension of the latter by Essmann et al. [42], which is usually referred to as the smooth particle mesh Ewald (SPME) method. 

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