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arXiv · 2305.05369

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

Jiuyang Liang·Zhenli Xu·Qi Zhou
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Abstract

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 u-series 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 $\mathcal{O}(b^{-M})$ for the energy and $\mathcal{O}(b^{-3M})$ 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.

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Jiuyang Liang, Zhenli Xu, Qi Zhou. 2023-05-09. Error estimate of the u-series method for molecular dynamics simulations. https://arxiv.org/abs/2305.05369

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