Completing density functional theory by machine learning hidden messages from molecules

Kohn–Sham density functional theory (DFT) is the basis of modern computational approaches to electronic structures. Their accuracy heavily relies on the exchange-correlation energy functional, which encapsulates electron–electron interaction beyond the classical model. As its universal form remains...

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Bibliographic Details
Published in:npj computational materials 2020-05, Vol.6 (1), Article 43
Main Authors: Nagai, Ryo, Akashi, Ryosuke, Sugino, Osamu
Format: Article
Language:English
Subjects:
639/301/1034/1038
639/638/563
639/766/119
Accuracy
Algorithms
Back propagation networks
Characterization and Evaluation of Materials
Chemistry and Materials Science
Computational Intelligence
Computer applications
Density functional theory
Learning algorithms
Machine learning
Materials Science
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Neural networks
Theoretical
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Summary:Kohn–Sham density functional theory (DFT) is the basis of modern computational approaches to electronic structures. Their accuracy heavily relies on the exchange-correlation energy functional, which encapsulates electron–electron interaction beyond the classical model. As its universal form remains undiscovered, approximated functionals constructed with heuristic approaches are used for practical studies. However, there are problems in their accuracy and transferability, while any systematic approach to improve them is yet obscure. In this study, we demonstrate that the functional can be systematically constructed using accurate density distributions and energies in reference molecules via machine learning. Surprisingly, a trial functional machine learned from only a few molecules is already applicable to hundreds of molecules comprising various first- and second-row elements with the same accuracy as the standard functionals. This is achieved by relating density and energy using a flexible feed-forward neural network, which allows us to take a functional derivative via the back-propagation algorithm. In addition, simply by introducing a nonlocal density descriptor, the nonlocal effect is included to improve accuracy, which has hitherto been impractical. Our approach thus will help enrich the DFT framework by utilizing the rapidly advancing machine-learning technique.
ISSN:2057-3960
2057-3960
DOI:10.1038/s41524-020-0310-0