Semi-local machine-learned kinetic energy density functional with third-order gradients of electron density

Junji Seino, Ryo Kageyama, Mikito Fujinami, Yasuhiro Ikabata, Hiromi Nakai

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17 Citations (Scopus)


A semi-local kinetic energy density functional (KEDF) was constructed based on machine learning (ML). The present scheme adopts electron densities and their gradients up to third-order as the explanatory variables for ML and the Kohn-Sham (KS) kinetic energy density as the response variable in atoms and molecules. Numerical assessments of the present scheme were performed in atomic and molecular systems, including first- and second-period elements. The results of 37 conventional KEDFs with explicit formulae were also compared with those of the ML KEDF with an implicit formula. The inclusion of the higher order gradients reduces the deviation of the total kinetic energies from the KS calculations in a stepwise manner. Furthermore, our scheme with the third-order gradient resulted in the closest kinetic energies to the KS calculations out of the presented functionals.

Original languageEnglish
Article number241705
JournalJournal of Chemical Physics
Issue number24
Publication statusPublished - 2018 Jun 28


ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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