An SO(3)-equivariant reciprocal-space neural potential for long-range interactions

• URL: http://arxiv.org/abs/2603.18389v2
• Date: Fri, 20 Mar 2026 03:13:49 GMT
• Title: An SO(3)-equivariant reciprocal-space neural potential for long-range interactions
• Abstract summary: Long-range electrostatic and polarization interactions play a central role in molecular and condensed-phase systems.<n>Modern SO(3)-equivariant neural potentials achieve high accuracy for short-range chemistry, but cannot represent the anisotropic, slowly decaying multipolar correlations governing realistic materials.<n>Here we introduce EquiEwald, a unified neural interatomic potential that embeds an Ewald-inspired reciprocal-space formulation within an irreducible SO(3)-equivariant framework.
• Score: 84.08721947253646
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Long-range electrostatic and polarization interactions play a central role in molecular and condensed-phase systems, yet remain fundamentally incompatible with locality-based machine-learning interatomic potentials. Although modern SO(3)-equivariant neural potentials achieve high accuracy for short-range chemistry, they cannot represent the anisotropic, slowly decaying multipolar correlations governing realistic materials, while existing long-range extensions either break SO(3) equivariance or fail to maintain energy-force consistency. Here we introduce EquiEwald, a unified neural interatomic potential that embeds an Ewald-inspired reciprocal-space formulation within an irreducible SO(3)-equivariant framework. By performing equivariant message passing in reciprocal space through learned equivariant k-space filters and an equivariant inverse transform, EquiEwald captures anisotropic, tensorial long-range correlations without sacrificing physical consistency. Across periodic and aperiodic benchmarks, EquiEwald captures long-range electrostatic behavior consistent with ab initio reference data and consistently improves energy and force accuracy, data efficiency, and long-range extrapolation. These results establish EquiEwald as a physically principled paradigm for long-range-capable machine-learning interatomic potentials.

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