Zero-Dipole Summation Method for Precisely Estimating Electrostatic Interactions in Molecular Simulation

Abstract

For computational studies of materials in a realistic manner, appropriate treatment of the Coulombic interaction is critical. Since the potential function is long-range and has both positive and negative signatures, it is not simple to handle the interaction in an effective manner, i.e., with high accuracy, low computational cost, freedom from artifacts, and ease of implementation. We introduce a novel idea, zero-dipole summation, for evaluating the electrostatic energy of classical particle system. The summation prevents the nonzero-charge and nonzero-dipole states artificially generated by simple cutoff truncation, which causes energetic noise and several artifacts. The currently derived energy formula nevertheless takes a simple pairwise form, which utilizes the cutoff procedure but employs a pairwise function changed from the pure Coulomb formula into a new formula taking account of the neutrality of charges and dipoles in the cutoff sphere (Fukuda et al. (2011) J. Chem. Phys. 134, 164107). This simple pairwise form enables us to effectively apply the scheme to high-performance computation. We discuss the theoretical details of our method and investigate the accuracy, stability, and static and dielectric properties of molecular systems via molecular dynamics simulation. We obtained the electrostatic energy error to be 0.01% at practical cutoff distance for an ionic system and a water system. We estimated the radial distribution function and the distant dependent Kirkwood factor for the water system, and confirmed the agreement with those by the Ewald method. Since the Kirkwood factor is very sensitive to the treatment of the electrostatic interaction, the agreement suggests that our method should be distinguishable from many other cutoff-like methods, which often cause the significant disagreement. Accurate electrostatic energies were also calculated with our method for a membrane protein with explicit ions and membrane and water molecules.