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arXiv · 2203.15025

Systematic derivation of angular--averaged Ewald potential

G. S. Demyanov·P. R. Levashov
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Abstract

In this work we provide a step by step derivation of an angular--averaged Ewald potential suitable for numerical simulations of disordered Coulomb systems. The potential was first introduced by E.\,Yakub and C.\,Ronchi without a clear derivation. Two methods are used to find the coefficients of the series expansion of the potential: based on the Euler--Maclaurin and Poisson summation formulas. The expressions for each coefficient is represented as a finite series containing derivatives of Jacobi theta functions. We also demonstrate the formal equivalence of the Poisson and Euler--Maclaurin summation formulas in the three-dimensional case. The effectiveness of the angular--averaged Ewald potential is shown by the example of calculating the Madelung constant for a number of crystal lattices.

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G. S. Demyanov, P. R. Levashov. 2022-03-28. Systematic derivation of angular--averaged Ewald potential. https://doi.org/10.1088/1751-8121%2Fac870b

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