SOFI: Finding point group symmetries in atomic clusters as finding the set of degenerate solutions in a shape-matching problem

TL;DR

SOFI is a novel algorithm that automates the detection of point group symmetries in atomic clusters by framing it as a shape-matching problem, improving accuracy and efficiency in symmetry identification.

Contribution

The paper introduces SOFI, a new algorithm that formulates point group symmetry detection as a degenerate shape-matching problem, outperforming existing methods.

Findings

SOFI effectively identifies PG symmetries in atomic clusters.

Compared to three other algorithms, SOFI shows superior accuracy.

The algorithm is publicly available as part of the IRA library.

Abstract

Point Group (PG) symmetries play a fundamental role in many aspects of theoretical chemistry and computational materials science. With the objective to automatize the search of PG symmetry operations of generic atomic clusters, we present a new algorithm called Symmetry Operation FInder (SOFI). SOFI addresses the problem of identifying PG symmetry by framing it as a degenerate shape-matching problem, where the multiple solutions correspond to distinct symmetry operations. The developed algorithm is compared against three other algorithms dedicated to PG identification, on a large set of atomic clusters. The results, along with some illustrative use cases, showcase the effectiveness of SOFI. The SOFI algorithm is released as part of the IRA library, accessible at https://github.com/mammasmias/IterativeRotationsAssignments.