Molecular dynamics scheme for precise estimation of electrostatic interaction via zero-dipole summation principle

Abstract

We propose a novel idea, zero-dipole summation, for evaluating the electrostatic energy of a classical particle system, and have composed an algorithm for effectively utilizing the idea for molecular dynamics. It conceptually prevents the nonzero-charge and nonzero-dipole states artificially generated by a simple cutoff truncation. The resulting energy formula is nevertheless represented by a simple pairwise function sum, which enables facile application to high-performance computation. By following a heuristic approach to derive the current electrostatic energy formula, we developed an axiomatic approach to construct the method consistently. Explorations of the theoretical details of our method revealed the structure of the generated error, and we analyzed it by comparisons with other methods. A numerical simulation using liquid sodium chloride confirmed that the current method with a small damping factor yielded sufficient accuracy with a practical cutoff distance region. The current energy function also conducts stable numerical integration in a liquid MD simulation. Our method is an extension of the charge neutralized summation developed by Wolf et al. [J. Chem. Phys. 110, 8254 (1999)]. Furthermore, we found that the current method becomes a generalization of the preaveraged potential method proposed by Yakub and Ronchi [J. Chem. Phys. 119, 11556 (2003)], which is based on a viewpoint different from the neutrality. The current study presents these relationships and suggests possibilities for their further applications.

A critical appraisal of the zero-multipole method: Structural, thermodynamic, dielectric, and dynamical properties of a water system

“…The discrepancy becomes small as increasing the cutoff length or the moment l on average. This behavior is similar to that observed in the NaCl crystal, 30,31 which has zero charge and zero dipole in the basic cell.…”

“…The efficiency of the ZMM has been validated as for the dipole moment (viz., the first-order multipole) at first. It has been investigated in applications to fundamental systems, such as ionic systems 31 and bulk water, 32 and the energy accuracy and the stability in MD simulation were confirmed. It has also been applied to biomolecules, such as DNA 33 or membrane protein, 34,35 with explicit water solvent, where the accuracies of energetic and dynamical properties have been confirmed by comparing with the SPME method.…”

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

“…Cutoff methods, where the interactions over a threshold distance are neglected or approximated, are also used. A zero-dipole method (Fukuda et al 2011) (or zeromultipole method generally) (Fukuda 2013) for the periodic boundary condition has recently been developed as an extension of the cutoff method. The zero-dipole method is implemented to take advantage of massively parallelized computational resource rather than PME because it needs less communication for parallelization.…”

Treating electrostatics with Wolf summation in combined quantum mechanical and molecular mechanical simulations

“…Newer developments based on the Wolf scheme include "force-switching Wolf" (FSw-Wolf) 38 of Yonezawa et al, the ZD approach of Fukuda et al that extends the idea of cutoff sphere neutralization from monopole to dipole, 31 the "longrange Wolf" method, 29 in which the compensation charge monopole is replaced by a Gaussian charge distribution in conjunction with "dipole neutralization", and most recently Fanouragakis' polynomial damping functions instead of error functions for splitting the short-and long-range interactions in Wolf summation. 30 Despite the popularity of the method, we note that the related developments and applications have so far been limited to classical mechanics; therefore, the performance of Wolf summation to describe long-range electrostatics for chemically reactive systems, which require uses of quantum mechanical potentials, remains unknown.…”

“…Besides the IPS method, a variety of cutoff-based algorithms, collectively referred to as non-Ewald methods, 23 has been developed for computation of electrostatics in classical simulations. These include the reaction field method, 24,25 the Wolf summation 26 and variants, [27][28][29][30] the zero dipole (ZD) summation method, 31 CHARMM switching/shifting functions, 32,33 and a series of methods under the generalized shifted force (SF) scheme. 32,[34][35][36][37] An important line in the development of non-Ewald methods is along the insightful work of Wolf et al, 26 who traced the origin of artifacts in simple electrostatic truncation to the existence of net charges within the cutoff spheres.…”