Solid-angle based nearest-neighbor algorithm adapted for systems with low coordination number

TL;DR

This paper introduces a geometric modification to the solid-angle-based nearest-neighbor (SANN) algorithm, called mSANN, which improves neighbor identification in systems with low coordination numbers without adding free parameters.

Contribution

The paper proposes the inscribed circle modification to enhance SANN's accuracy in low-coordination systems, providing a parameter-free, robust, and computationally efficient neighbor identification method.

Findings

mSANN outperforms original SANN in low-coordination systems.

The modified algorithm is robust across 2D and 3D systems.

Benchmark results show improved accuracy over Voronoi methods.

Abstract

Nearest-neighbor identification is central to the analysis of local structure in condensed matter systems. The solid-angle-based nearest-neighbor (SANN) algorithm is widely used offering a parameter-free and computationally efficient alternative to cutoff- or Voronoi-based methods. Unfortunately, however, in systems with low coordination numbers, SANN tends to identify many particles as neighbors that are outside the nearest neighbor shell. Here, we propose a solution to this problem. Specifically, we propose a geometric modification, the ``inscribed circle modification'', that resolves systematic overcounting in low-coordination lattices without introducing free parameters. We benchmark the modified algorithm (mSANN) against Voronoi and the original SANN algorithm in crystalline, quasicrystalline, and heterogeneous systems, and demonstrate that it provides robust and low-cost neighbor identification across both two and three dimensions.