This paper provides an error estimate for the u-series decomposition 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.

翻译：本文对分子动力学模拟中库仑相互作用的u系列分解进行了误差估计。我们证明了u系列中截断高斯项数$M$和双边序列逼近中插值节点基数$b$是影响算法精度的两个关键参数，且能量误差以$\mathcal{O}(b^{-M})$收敛，力误差以$\mathcal{O}(b^{-3M})$收敛。同时得到了静电能量和力中由数值积分和截断引起的误差界。此外，还提供了封闭形式的公式，这些公式有助于在给定精度下进行模拟参数设置。通过对两个实际系统的误差分析验证了上述结果。