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Strict derivation of angular-averaged Ewald potential | | G. S. Demyanov
; P. R. Levashov
; | | Date: |
28 Mar 2022 | | Abstract: | In this work we strictly derive 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 strict mathematical
justification. 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. | | Source: | arXiv, 2203.15025 | | Services: | Forum | Review | PDF | Favorites | |
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