Ewald methods

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... 

Fig. 6.21 The construction of a system of periodic cells in the Ewald method. (Figure adapted from Allen M P and D ] Tildesley 1987. Computer Simulation of Liquids, Oxford, Oxford University Press.)...

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. 

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. 

Variational electrostatic projection method. In some instances, the calculation of PMF profiles in multiple dimensions for complex chemical reactions might not be feasible using full periodic simulation with explicit waters and ions even with the linear-scaling QM/MM-Ewald method [67], To remedy this, we have developed a variational electrostatic projection (VEP) method [75] to use as a generalized solvent boundary potential in QM/MM simulations with stochastic boundaries. The method is similar in spirit to that of Roux and co-workers [76-78], which has been recently... 

The fourth term on the right-hand side of eq. (11.3) is the electrostatic interaction (Coulomb s law) between pairs of charged atoms i and j, separated by distance r j. Since electrostatic interactions fall off slowly with r (only as r-1) they are referred to as long-range and, for an infinite system such as a periodic solid, special techniques, such as the Ewald method, are required to sum up all the electrostatic interactions (cf. Section 7.1) (see e.g. Leach, Jensen (Further reading)). The... 

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. 

An analogous implementation for the standard Ewald method has been presented [44]. Conversely, direct use of the Ewald sum [45] or approximations to it [46 18], which are pairwise decomposable and hence suitable for MC simulations, have generally proven to be too inefficient for most modern applications [49]. Additionally, it should be pointed out that Ewald sums — independent of implementation — are incompatible with implicit solvent models that model a spatially varying dielectric with anything more than trivial functional dependencies [45]. 

Because of the long-range nature of the dipolar interaction, care must be taken in the evaluation of the dipolar field. For hnite systems the sums in Eq. (3.12) are performed over all particles in the system. Eor systems with periodic boundary conditions the Ewald method [57-59], can be used to correctly calculate the conditionally convergent sum involved. However, in most work [12,13] the simpler Lorentz-cavity method is used instead. 

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