### Abstract

We propose a machine-learned correlation model that is built using the regression between density variables such as electron density and correlation energy density. The correlation energy density of coupled cluster singles, doubles, and perturbative triples [CCSD(T)] is derived based on grid-based energy density analysis. The complete basis set (CBS) limit is estimated using the composite method, which has been reported to calculate the total correlation energy. The numerical examination revealed that the correlation energy density of the CCSD(T)/CBS level is appropriate for the response variable of machine learning. In addition to the density variables used in the exchange-correlation functionals of the density functional theory, the Hartree-Fock (HF) exchange energy density and electron density based on the fractional occupation number of molecular orbitals were employed as explanatory variables. Numerical assessments confirmed the accuracy and efficiency of the present correlation model. Consequently, the present protocol, namely, learning the CCSD(T)/CBS correlation energy density using density variables obtained by the HF calculation with a small basis set, yields an efficient correlation model.

Original language | English |
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Article number | 024104 |

Journal | Journal of Chemical Physics |

Volume | 151 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2019 Jul 14 |

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### ASJC Scopus subject areas

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

### Cite this

**Machine-learned electron correlation model based on correlation energy density at complete basis set limit.** / Nudejima, Takuro; Ikabata, Yasuhiro; Seino, Junji; Yoshikawa, Takeshi; Nakai, Hiromi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Machine-learned electron correlation model based on correlation energy density at complete basis set limit

AU - Nudejima, Takuro

AU - Ikabata, Yasuhiro

AU - Seino, Junji

AU - Yoshikawa, Takeshi

AU - Nakai, Hiromi

PY - 2019/7/14

Y1 - 2019/7/14

N2 - We propose a machine-learned correlation model that is built using the regression between density variables such as electron density and correlation energy density. The correlation energy density of coupled cluster singles, doubles, and perturbative triples [CCSD(T)] is derived based on grid-based energy density analysis. The complete basis set (CBS) limit is estimated using the composite method, which has been reported to calculate the total correlation energy. The numerical examination revealed that the correlation energy density of the CCSD(T)/CBS level is appropriate for the response variable of machine learning. In addition to the density variables used in the exchange-correlation functionals of the density functional theory, the Hartree-Fock (HF) exchange energy density and electron density based on the fractional occupation number of molecular orbitals were employed as explanatory variables. Numerical assessments confirmed the accuracy and efficiency of the present correlation model. Consequently, the present protocol, namely, learning the CCSD(T)/CBS correlation energy density using density variables obtained by the HF calculation with a small basis set, yields an efficient correlation model.

AB - We propose a machine-learned correlation model that is built using the regression between density variables such as electron density and correlation energy density. The correlation energy density of coupled cluster singles, doubles, and perturbative triples [CCSD(T)] is derived based on grid-based energy density analysis. The complete basis set (CBS) limit is estimated using the composite method, which has been reported to calculate the total correlation energy. The numerical examination revealed that the correlation energy density of the CCSD(T)/CBS level is appropriate for the response variable of machine learning. In addition to the density variables used in the exchange-correlation functionals of the density functional theory, the Hartree-Fock (HF) exchange energy density and electron density based on the fractional occupation number of molecular orbitals were employed as explanatory variables. Numerical assessments confirmed the accuracy and efficiency of the present correlation model. Consequently, the present protocol, namely, learning the CCSD(T)/CBS correlation energy density using density variables obtained by the HF calculation with a small basis set, yields an efficient correlation model.

UR - http://www.scopus.com/inward/record.url?scp=85068784481&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068784481&partnerID=8YFLogxK

U2 - 10.1063/1.5100165

DO - 10.1063/1.5100165

M3 - Article

AN - SCOPUS:85068784481

VL - 151

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 2

M1 - 024104

ER -