Optimized Periodic Coulomb Potential in Two Dimension

TL;DR

This paper introduces a numerically optimized method for calculating the two-dimensional Coulomb potential with periodic boundary conditions, achieving higher precision and efficiency than traditional approaches like Ewald summation.

Contribution

The authors develop a new optimized potential approach using polynomial splines and reciprocal space summation, improving accuracy and computational speed for 2D periodic Coulomb calculations.

Findings

Optimized potentials outperform Ewald in precision by several orders of magnitude.

Explicit simple expressions enable fast calculations with minimal reciprocal space terms.

The method is applicable for high-precision simulations of 2D periodic systems.

Abstract

The 1/r Coulomb potential is calculated for a two dimensional system with periodic boundary conditions. Using polynomial splines in real space and a summation in reciprocal space we obtain numerically optimized potentials which allow us efficient calculations of any periodic (long-ranged) potential up to high precision. We discuss the parameter space of the optimized potential for the periodic Coulomb potential. Compared to the analytic Ewald potential, the optimized potentials can reach higher precisions by up to several orders of magnitude. We explicitly give simple expressions for fast calculations of the periodic Coulomb potential where the summation in reciprocal space is reduced to a few terms.