Ewald summation-based methods

In comparison, the Ewald summation-based methods were developed for the periodic boundary treatment, where the entire system plus its solvent environment are explicitly represented. Thus, Ewald summation-based simulations are particularly suited for studying free energy changes that involve delocalized... 

Zhang, P., Truhlar, D. G., and Gao, J. (2012). Fragment-based quantum mechanical methods for periodic systems with Ewald summation and mean image charge convention for long-range electrostatic interactions, Phys. Chem. Chem. Phys. 14(21), 7821-7829. 

A variety of methods are available for computing electrostatic energies (and forces), including the Fast Multipole Method [38], the Particle-Particle-Particle-Mesh Method [179], and methods based on the technique of Ewald Summation [125, 367] we only discuss a particular variant of the latter approach here and not... 

The intramolecular van der Waal interactions were calculated only between atoms that were located at distances greater than their fourth nearest neighbors. A modified Ewald summation method (Karasawa and Goddard 1989) was used for calculating the nonbonded coulomb interactions, and an atom-based direct cutoff method was used for van der Waal interactions. Smart minimizer, as implemented in Cerius /Material Studio, was used for geometry optimization. The optimization was considered to be converged when a gradient of 0.0001 kcal/mole was reached. 

Molecular dynamics was performed at constant temperature with AMBER 4.1 all-atom force field [121] and Particle Mesh Ewald method (PME) was used for the calculation of electrostatic interactions [122]. This is a fast implementation of the Ewald summation method for calculating the full electrostatic energy of a unit cell in a macroscopic lattice of repeating images. The PME grid spacing was 1.0A. It was interpolated on a cubic B-spline, with the direct set tolerance set to 0.000001. Periodic boundary conditions were imposed in all directions. All solute-solute non-bonded interactions were calculated without jmy cut-off distance, while a non-bonded residue based cutoff distance of 9A was used for the solvent-solvent and for the solute-solvent interactions. The non-bonded pair list was updated every 20 steps and the... 

The reason Eq. (F.18) is often preferred is that it is based on the total potential (r) obtained from Eq. (F.17), which is valid everywhere in the crystal except at the positions of the ions. Use the Ewald summation method to calcnlate the Madelnng energy per unit cell of the NaCl crystal. How many shells do yon need to inclnde for convergence of the Madelung energy to one part in 10 Verify, by using a few different valnes of a, that the final answer does not depend on this parameter (but the number of terms required to reach the desired convergence may depend on it). 

In this article, we restrict ourselves to the description of these three methods for nonperiodic systems. There are near-linear scaling methods for periodic systems based on the Ewald summation procedure (see Toukmaji and Board for a... 

A large number of crystal and NMR structures are available for DNA double-.stranded helices in the environment dependent A-, B-, or Z-forms. Since the first study reported by Levitt in 1983, several MD studies have been conducted on various DNA sequences. As the number of MD simulations increa.sed with available computational means, simulations under in vacuo conditions as well as those using various truncation schemes for the evaluation of the long-range electrostatic interactions have revealed their limits (.see Methodology). New methods, based on the Ewald summation procedure, have been developed and applied to the simulation of nucleic acid duplexes in the crystal phase and in aqueous solution. We will, in the following, report mostly on studies incorporating such advances. Previous work is reviewed in Refs. 2, 4-6, and 8. 

Regardless of the type of model used, a method must be chosen for the self-consistent solution of the polarizable degrees of freedom. Direct solution via matrix inversion is nearly always avoided by most researchers in the field, because of the prohibitive O(N ) scaling with system size, N. Both iterative and predictive methods reduce the scaling to match that of the potential evaluation [O(N ) for direct summation 0(N In N) for Ewald-based meth-ods ° " 0 N) if interactions are neglected beyond some distance cutoff], but the cost of the iterations means that the predictive methods are always more efficient. Extended Lagrangian methods have been implemented for all four types of polarizable... 

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