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.