A fuzzy classification framework to identify equivalent atoms in complex materials and molecules

The nature of an atom in a bonded structure—such as in molecules, in nanoparticles, or in solids, at surfaces or interfaces—depends on its local atomic environment. In atomic-scale modeling and simulation, identifying groups of atoms with equivalent environments is a frequent task, to gain an understanding of the material function, to interpret experimental results, or to simply restrict demanding first-principles calculations. However, while routine, this task can often be challenging for complex molecules or non-ideal materials with breaks in symmetries or long-range order. To automatize this task, we here present a general machine-learning framework to identify groups of (nearly) equivalent atoms. The initial classification rests on the representation of the local atomic environment through a high-dimensional smooth overlap of atomic positions (SOAP) vector. Recognizing that not least thermal vibrations may lead to deviations from ideal positions, we then achieve a fuzzy classification by mean-shift clustering within a low-dimensional embedded representation of the SOAP points as obtained through multidimensional scaling. The performance of this classification framework is demonstrated for simple aromatic molecules and crystalline Pd surface examples.