Particle-mesh-Ewald method

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. 

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. 

Cheatham T. E., Ill, Miller J. L, FoxT., Darden T. A. and Kollman P. A. Molecular dynamics simulations on solvated biomolecu-lar systems the particle mesh Ewald method leads to stable trajectories of DNA, RNA, and proteins. J. Am. Chem. Soc. (1995) 117(14) 4193-4194. 

The probably most delicate aspect of nucleic-acid modeling is the treatment of long-range interactions. The particle-mesh Ewald method, introduced by Darden et al. [109] [110] has yielded very promising results in a number of recent molecular-dynamics simulations of oligonucleotides... 

The motions of proteins are usually simulated in aqueous solvent. The water molecules can be represented either explicitly or implicitly. To include water molecules explicitly implies more time-consuming calculations, because the interactions of each protein atom with the water atoms and the water molecules with each other are computed at each integration time step. The most expensive part of the energy and force calculations is the nonbonded interactions because these scale as 77 where N is the number of atoms in the system. Therefore, it is common to neglect nonbonded interactions between atoms separated by more than a defined cut-off ( 10 A). This cut-off is questionable for electrostatic interactions because of their 1/r dependence. Therefore, in molecular dynamics simulations, a Particle Mesh Ewald method is usually used to approximate the long-range electrostatic interactions (71, 72). 

Petersen HG. Accuracy and efficiency of the particle mesh Ewald method. J. Chem. Phys. 1995 103 3668-3679. 

In recent years, a number of models have been introduced which permit the inclusion of long-range electrostatic interactions in molecular dynamics simulation. For simulations of proteins and enzymes in a crystalline state, the Ewald summation is considered to be the correct treatment for long range electrostatic interactions (Ewald 1921 Allen and Tildesley 1989). Variations of the Ewald method for periodic systems include the particle-mesh Ewald method (York et al. 1993). To treat non-periodic systems, such as an enzyme in solution other methods are required. Kuwajima et al. (Kuwajima and Warshel 1988) have presented a model which extends the Ewald method to non-periodic systems. Other methods for treating explicitly long-range interactions... 

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. 

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. 

Within the last decade important progress has been made in the reliability of MD simulations of solvated nucleic acids using improved force fields and, in particular, a better treatment of electrostatics by the particle-mesh Ewald method. For the first time unrestrained simulations have become possible. Starting out firom experimental geometries it is now possible to explore the conformational space in the vicinity of the starting geometry and to study conformational transitions. ... 

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. 

By having written a point-multipole as the spherical tensor gradients passing through a point, one easily derives the particle mesh Ewald method for point multipoles. The main differences occur in the calculation of the structure factor, which requires spherical tensor gradients of the Cardinal B-spline weight, and the calculation of the short-range real-space correction (see Section 1.6.3). 

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. 

---