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Exact constraints and appropriate norms in machine-learned exchange-correlation functionals

Pokharel, Kanun; Furness, James William; Yao, Yi; Blum, Volker; Irons, Tom James Patrick; Teale, Andrew Michael; Sun, Jianwei

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Kanun Pokharel

James William Furness

Yi Yao

Volker Blum

Tom James Patrick Irons

Professor of Computational and Theoretical Chemistry

Jianwei Sun


Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human-designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently, efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to de-orbitalize the strongly constrained and appropriately normed (SCAN) functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding the use of the orbital-dependent kinetic energy density. The performance and transferability of the machine-learned functional are demonstrated for molecular and periodic systems.


Pokharel, K., Furness, J. W., Yao, Y., Blum, V., Irons, T. J. P., Teale, A. M., & Sun, J. (2022). Exact constraints and appropriate norms in machine-learned exchange-correlation functionals. Journal of Chemical Physics, 157(17), Article 174106.

Journal Article Type Article
Acceptance Date Oct 9, 2022
Online Publication Date Nov 3, 2022
Publication Date Nov 7, 2022
Deposit Date Nov 8, 2022
Publicly Available Date Nov 10, 2022
Journal The Journal of Chemical Physics
Print ISSN 0021-9606
Electronic ISSN 1089-7690
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 157
Issue 17
Article Number 174106
Keywords Physical and Theoretical Chemistry; General Physics and Astronomy
Public URL
Publisher URL


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