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

05/09/2023

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by   Jiuyang Liang, et al.

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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 𝒪(b^-M) for the energy and 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.