Error estimate of the u-series method for molecular dynamics simulations

JY Liang and ZL Xu and Q Zhou, APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 77, 101759 (2025).

DOI: 10.1016/j.acha.2025.101759

This paper provides an error estimate for the u-series method of the Coulomb interaction in molecular dynamics simulations. We show that the number of truncated Gaussians M in the useries and the base of interpolation nodes b in the bilateral serial approximation are two key parameters for the algorithm accuracy, and that the errors converge as (9(b-M) for the energy and (9(b-3M) for the force. Error bounds due to numerical quadrature and cutoff in both the electrostatic energy and forces are obtained. Closed-form formulae are also provided, which are useful in the parameter setup for simulations under a given accuracy. The results are verified by analyzing the errors of two practical systems.

Return to Publications page