Abstract
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 language | English |
|---|---|
| Article number | 241705 |
| Journal | Journal of Chemical Physics |
| Volume | 148 |
| Issue number | 24 |
| DOIs | |
| Publication status | Published - 2018 Jun 28 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry
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Semi-local machine-learned kinetic energy density functional with third-order gradients of electron density. / Seino, Junji; Kageyama, Ryo; Fujinami, Mikito; Ikabata, Yasuhiro; Nakai, Hiromi.
In: Journal of Chemical Physics, Vol. 148, No. 24, 241705, 28.06.2018.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Semi-local machine-learned kinetic energy density functional with third-order gradients of electron density
AU - Seino, Junji
AU - Kageyama, Ryo
AU - Fujinami, Mikito
AU - Ikabata, Yasuhiro
AU - Nakai, Hiromi
PY - 2018/6/28
Y1 - 2018/6/28
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85044043266&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85044043266&partnerID=8YFLogxK
U2 - 10.1063/1.5007230
DO - 10.1063/1.5007230
M3 - Article
AN - SCOPUS:85044043266
VL - 148
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
SN - 0021-9606
IS - 24
M1 - 241705
ER -