A Fuzzy Classification Framework to Identify Equivalent Atoms in Complex Materials and Molecules

TL;DR

This paper introduces a machine-learning framework that uses fuzzy classification and SOAP vectors to identify equivalent atoms in complex materials, accounting for thermal vibrations and structural deviations.

Contribution

It presents a novel combination of SOAP-based representation and mean-shift clustering for fuzzy classification of atoms in complex structures, improving identification accuracy.

Findings

Effective in classifying atoms in aromatic molecules

Successfully applied to crystalline Pd surfaces

Handles thermal vibrations and structural deviations

Abstract

The nature of an atom in a bonded structure -- such as in molecules, in nanoparticles or 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. While routine, this task can often be challenging for complex molecules or non-ideal materials with breaks of 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.