General Atomic Neighborhood Fingerprint for Machine Learning-Based Methods

To facilitate chemical space exploration for material screening or to accelerate computationally expensive first-principles simulations, inexpensive surrogate models that capture electronic, atomistic, or macroscopic materials properties have become an increasingly popular tool over the last decade. The most fundamental quantity common across all such machine learning (ML)-based methods is the fingerprint used to numerically represent a material or its structure. To increase the learning capability of the ML methods, the common practice is to construct fingerprints that satisfy the same symmetry relations as displayed by the target material property of interest (for which the ML model is being developed). Thus, in this work, we present a general, simple, and elegant fingerprint that can be used to learn different electronic/atomistic/structural properties, irrespective of their scalar, vector, or tensorial nature. This fingerprint is based on the concept of multipole terms and can be systematically increased in sophistication to achieve a desired level of accuracy. Using the examples of Al, C, and hafnia (HfO₂), we demonstrate the applicability of this fingerprint to easily classify different atomistic environments, such as phases, surfaces, point defects, and so forth. Furthermore, we demonstrate the generality and effectiveness of this fingerprint by building an accurate, yet inexpensive, ML-based potential energy model for the case of Al using a reference data set that is obtained from density functional theory computations. Finally, we note that the fingerprint definition presented here has applications in fields beyond materials informatics, such as structure prediction, identification of defects, and detection of new crystal phases.