On machine learnability of local contributions to interatomic potentials from density functional theory calculations

Machine learning interatomic potentials, as a modern generation of classical force fields, take atomic environments as input and predict the corresponding atomic energies and forces. We challenge the commonly accepted assumption that the contribution of an atom can be learned from the short-range local environment of that atom. We employ density functional theory calculations to quantify the decay of the induced electron density and electrostatic potential in response to local perturbations throughout insulating, semiconducting and metallic samples of different dimensionalities. Molecules and thin layers are shown to fail keeping such disturbances localized. Therefore, the learnability of local atomic contributions, which guarantees scalability and transferability of a machine learning interatomic potential, is questionable in the case of molecules and low-dimensional samples. Similarly, the induced electrostatic effects due to substituted impurities or vacancy sites in a crystalline bulk are weakly damped and remain significant beyond several interatomic distances. However, geometric deformations in bulks are practically local within the first neighbors and induce a Yukawa-type electrostatic potential that exponentially vanishes. The practical importance of this finding is that it limits the application of the machine learning interatomic potentials to conformational search or thermal properties of bulk materials and so on, where only purely geometrical deformations are involved. Once chemically impactful defects like aliovalent impurities or vacancies are present, the interatomic potentials trained on local environments need to be corrected for long-range effects.