Cascading symmetry constraint during machine learning-enabled structural search for sulfur induced Cu(111)-$(\sqrt{43}\times\sqrt{43})$ surface reconstruction

In this work, we investigate how exploiting symmetry when creating and modifying structural models may speed up global atomistic structure optimization. We propose a search strategy in which models start from high symmetry configurations and then gradually evolve into lower symmetry models. The algorithm is named cascading symmetry search and is shown to be highly efficient for a number of known surface reconstructions. We use our method for the sulfur induced Cu (111) $(\sqrt{43}\times\sqrt{43})$ surface reconstruction for which we identify a new highly stable structure which conforms with experimental evidence.