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

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 iterative rotations and assignments library, accessible at https://github.com/mammasmias/IterativeRotationsAssignments.