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

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.