TY - JOUR

T1 - Order- N orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals

AU - Imoto, Fumihiro

AU - Imada, Masatoshi

AU - Oshiyama, Atsushi

N1 - Publisher Copyright:
© 2021 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

PY - 2021/9

Y1 - 2021/9

N2 - Orbital-free density-functional theory (OFDFT) offers a challenging way of electronic-structure calculations scaled as O(N) computation for system size N. We here develop a scheme of the OFDFT calculations based on the accurate and transferrable kinetic-energy density-functional (KEDF), which is created in an unprecedented way using appropriately constructed neural network (NN). We show that our OFDFT scheme reproduces the electron density obtained in the state-of-the-art DFT calculations and then provides accurate structural properties of 24 different systems, ranging from atoms, molecules, metals, semiconductors, and an ionic material. The accuracy and the transferability of our KEDF is achieved by our NN training system in which the kinetic-energy functional derivative (KEFD) at each real-space grid point is used. The choice of the KEFD as a set of training data is essentially important, because first it appears directly in the Euler equation, which one should solve, and second, its learning assists in reproducing the physical quantity expressed as the first derivative of the total energy. More generally, the present development of KEDF T[ρ] is in the line of systematic expansion in terms of the functional derivatives δℓ1T/δρℓ1 through progressive increase of ℓ1. The present numerical success demonstrates the validity of this approach. The computational cost of the present OFDFT scheme indeed shows the O(N) scaling, as is evidenced by the computations of the semiconductor SiC used in power electronics.

AB - Orbital-free density-functional theory (OFDFT) offers a challenging way of electronic-structure calculations scaled as O(N) computation for system size N. We here develop a scheme of the OFDFT calculations based on the accurate and transferrable kinetic-energy density-functional (KEDF), which is created in an unprecedented way using appropriately constructed neural network (NN). We show that our OFDFT scheme reproduces the electron density obtained in the state-of-the-art DFT calculations and then provides accurate structural properties of 24 different systems, ranging from atoms, molecules, metals, semiconductors, and an ionic material. The accuracy and the transferability of our KEDF is achieved by our NN training system in which the kinetic-energy functional derivative (KEFD) at each real-space grid point is used. The choice of the KEFD as a set of training data is essentially important, because first it appears directly in the Euler equation, which one should solve, and second, its learning assists in reproducing the physical quantity expressed as the first derivative of the total energy. More generally, the present development of KEDF T[ρ] is in the line of systematic expansion in terms of the functional derivatives δℓ1T/δρℓ1 through progressive increase of ℓ1. The present numerical success demonstrates the validity of this approach. The computational cost of the present OFDFT scheme indeed shows the O(N) scaling, as is evidenced by the computations of the semiconductor SiC used in power electronics.

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U2 - 10.1103/PhysRevResearch.3.033198

DO - 10.1103/PhysRevResearch.3.033198

M3 - Article

AN - SCOPUS:85115888334

SN - 2643-1564

VL - 3

JO - Physical Review Research

JF - Physical Review Research

IS - 3

M1 - 033198

ER -