**Two-body potential model based on cosine series expansion for ionic
materials**

T Oda and WJ Weber and H Tanigawa, COMPUTATIONAL MATERIALS SCIENCE, 111, 54-63 (2016).

DOI: 10.1016/j.commatsci.2015.08.055

A method to construct a two-body potential model for ionic materials with a Fourier series basis is examined. In this method, the coefficients of cosine basis functions are uniquely determined by solving simultaneous linear equations to minimize the sum of weighted mean square errors in energy, force and stress, where first-principles calculation results are used as the reference data. As a validation test of the method, potential models for magnesium oxide are constructed. The mean square errors appropriately converge with respect to the truncation of the cosine series. This result mathematically indicates that the constructed potential model is sufficiently close to the one that is achieved with the non-truncated Fourier series and demonstrates that this potential virtually provides minimum error from the reference data within the two-body representation. The constructed potential models work appropriately in both molecular statics and dynamics simulations, especially if a two-step correction to revise errors expected in the reference data is performed, and the models clearly outperform two existing Buckingham potential models that were tested. The good agreement over a broad range of energies and forces with first- principles calculations should enable the prediction of materials behavior away from equilibrium conditions, such as a system under irradiation. (C) 2015 Elsevier B.V. All rights reserved.

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