Machine-learning-based exchange correlation functional with physical asymptotic constraints

Abstract

Density functional theory is the standard theory for computing the electronic structure of materials, which is based on a functional that maps the electron density to the energy. However, a rigorous form of the functional is not known and has been heuristically constructed by interpolating asymptotic constraints known for extreme situations, such as isolated atoms and uniform electron gas. Recent studies have demonstrated that the functional can be effectively approximated using machine learning (ML) approaches. However, most ML models do not satisfy asymptotic constraints. In this paper, by applying a ML model architecture, we demonstrate a neural network-based exchange-correlation functional satisfying physical asymptotic constraints. Calculations reveal that the trained functional is applicable to various materials with an accuracy higher than that of existing functionals, even for materials whose electronic properties are not included in training dataset. Our proposed method thus improves the accuracy and generalization performance of the ML-based functional by combining the advantages of ML and analytical modeling.