2025/03/02 by J.V. Calara, Calara, Joven V., Jan D. Miller +1
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #Enzyme Structure and Function #FOS: Physical sciences #High-pressure geophysics and materials #Materials Science (cond-mat.mtrl-sci) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2503.00977
openalex publication_date 2025/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an absolutely convergent real-space method for evaluating Madelung potentials in ionic lattices. The method, based on repeated axial multipole units with systematically eliminated low-order moments, applies uniformly to bulk crystals, surfaces, edges, interstitial sites, and exterior points, without recourse to reciprocal-space techniques. In the RU-13 construction, the far-field contribution of each axial multipole unit decays as r^(-13), ensuring fast and absolute convergence of the real-space direct sum. The method yields identical limits under spherical and cubic summation geometries and reproduces standard Madelung constants with high precision, achieving 13-digit accuracy within a radius of 40 lattice spacings. Extensions to dimensions d = 1-6 exhibit convergence consistent with asymptotic decay predictions.