Non-Ewald methods for evaluating the electrostatic interactions of charge systems: similarity and difference

Abstract

In molecular simulations, it is essential to properly calculate the electrostatic interactions of particles in the physical system of interest. Here we consider a method called the non-Ewald method, which does not rely on the standard Ewald method with periodic boundary conditions, but instead relies on the cuto¤-based techniques. We focus on the physicochemical and mathematical conceptual aspects of the method in order to gain a deeper understanding of the simulation methodology.In particular, we take into account the reaction …eld (RF) method, the isotropic periodic sum (IPS) method, and the zero-multipole summation method (ZMM). These cuto¤-based methods are based on di¤erent physical ideas and are completely distinguishable in their underlying concepts. The RF and IPS methods are "additive" methods that incorporate information outside the cuto¤ region, via dielectric medium and isotropic boundary condition, respectively. In contrast, the ZMM is a "subtraction" method that tries to remove the arti…cial e¤ects, generated near the boundary, from the cuto¤ sphere. Nonetheless, we …nd physical and/or mathematical similarities between these methods. In particular, the modi…ed RF method can be derived by the principle of neutralization utilized in the ZMM, and we also found a direct relationship between IPS and ZMM.

Binding Mechanism of Riboswitch to Natural Ligand Elucidated by McMD-Based Dynamic Docking Simulations

“…NVT simulations were performed at 300 K using the Bussi thermostat, while the NPT simulations additionally used the Bussi barostat under 1 bar at 300 K. The long-range electrostatics were calculated using the zero-dipole summation method, which is a cutoff-based approach utilizing a well-defined pairwise function ,− with the damping factor α set to 0 Å –1 and the atom-based cutoff length set to 12 Å. A time-step of 2 fs was used, with LINCS to constrain the bond lengths and SETTLE to constrain the water geometries.…”

Pressure of Coulomb systems with volume-dependent long-range potentials

“…Many 'Non-Ewald' methods have been developed to calculate the electrostatic long-ranged interactions of charged systems [45] in order to speed up simulations. We now consider the method called 'pre-averaging' or 'angular-averaging' of the Ewald potential.…”

“…Next, we calculate the derivative of each term in sum (45) to obtain the derivative of U 2 with respect to L:…”

A Cutoff-based Method with Charge-distribution-data Driven Pair Potentials for Efficiently Estimating Electrostatic Interactions in Molecular System

“…It also has practical advantages such as using only O(N ) computational cost for large systems consisting of N particles 21,22 . Of course, the straight truncation cuto¤ is not used at present, due to causing signi…cant errors, but instead, the CB method with an appropriately prepared pair potential function is useful in molecular simulations [23][24][25][26][27][28] .…”

“…In discussing the relationship between these methods 28 , it has been shown that they de…ne an equivalence of energies in a certain limit of some parameter value included in each method.…”