Exact method for the simulation of Coulombic systems by spherically truncated, pairwise r−1 summation

Abstract

Based on a recent result showing that the net Coulomb potential in condensed ionic systems is rather short ranged, an exact and physically transparent method permitting the evaluation of the Coulomb potential by direct summation over the r−1 Coulomb pair potential is presented. The key observation is that the problems encountered in determining the Coulomb energy by pairwise, spherically truncated r−1 summation are a direct consequence of the fact that the system summed over is practically never neutral. A simple method is developed that achieves charge neutralization wherever the r−1 pair potential is truncated. This enables the extraction of the Coulomb energy, forces, and stresses from a spherically truncated, usually charged environment in a manner that is independent of the grouping of the pair terms. The close connection of our approach with the Ewald method is demonstrated and exploited, providing an efficient method for the simulation of even highly disordered ionic systems by direct, pairwise r−1 summation with spherical truncation at rather short range, i.e., a method which fully exploits the short-ranged nature of the interactions in ionic systems. The method is validated by simulations of crystals, liquids, and interfacial systems, such as free surfaces and grain boundaries.

Polar surface effects on the thermal conductivity of ZnO nanowires: a shell-like surface reconstruction-induced preserving mechanism

“…40 However, for surface-dominated nanomaterials such as NWs in the present work, the periodicity assumption is clearly violated, and therefore it is crucial to employ a truncation-based summation method. In this work, we have utilized the truncation-based summation approach initially proposed by Wolf et al in 1999 41 and further developed by Fennell and Gezelter in 2006. 42 A key development in the work by Fennell and Gezelter 42 was to ensure that the electrostatic force and potential are consistent with each other, while remaining continuous at the interatomic cut-off distance.…”

Simulation of screw dislocations in wadsleyite

“…Similar patterns of inwards displacements have also been observed for screw dislocations in MgO, forsterite (Walker et al, 2005b) and zeolite A (Walker et al, 2004) and it appears that the explanation may be rather general. (Wolf et al, 1999), are truncated at a radius of 16.0Å and damped using an η parameter of 0.2Å −1 . Sawamoto et al (1984), Ahrens (1995, Kumazawa and Anderson (1969), and Zha et al (1997).…”

“…The key difference in the formulation of the new model is that the Coulomb term is evaluated using a spherically truncated, pairwise, real space summation (Wolf et al, 1999). This allows calculations using the model to make use of physically intuitive and easily parallelizable spatial locality to realize linear scaling with system size (e.g.…”

Force-enhanced atomic refinement: Structural modeling with interatomic forces in a reverse Monte Carlo approach applied to amorphous Si andSiO2

“…3 stipulates that the Ewald summation 22 should be used in the calculation of the total energy and forces. However, as shown by Wolf et al 23 in a recent communication, a pairwise sum can be constructed in real space by ensuring charge neutrality of the system such that the sum produces results very similar to that obtained from the Ewald summation. We have adopted this real-space approach to calculate the total energy and forces via Wolf's summation.…”