Large-scale real-space density-functional calculations: Moiré-induced electron localization in graphene

2015 ◽  
Vol 117 (11) ◽  
pp. 112811 ◽  
Author(s):  
Atsushi Oshiyama ◽  
Jun-Ichi Iwata ◽  
Kazuyuki Uchida ◽  
Yu-Ichiro Matsushita
Keyword(s):  
Density Functional Calculations ◽  
Density Functional ◽  
Large Scale ◽  
Real Space ◽  
Electron Localization ◽  
Space Density

scholarly journals Tensor-structured algorithm for reduced-order scaling large-scale Kohn–Sham density functional theory calculations

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Chih-Chuen Lin ◽  
Phani Motamarri ◽  
Vikram Gavini
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Large Scale ◽  
Density Functional Theory Calculations ◽  
System Size ◽  
Real Space ◽  
Functional Theory ◽  
Reduced Order ◽  
Separable Approximation ◽  
Tensor Basis

AbstractWe present a tensor-structured algorithm for efficient large-scale density functional theory (DFT) calculations by constructing a Tucker tensor basis that is adapted to the Kohn–Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn–Sham Hamiltonian and an L1 localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system-size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2000 electrons.

scholarly journals Linear scaling algorithm of real-space density functional theory of electrons with correlated overlapping domains

2012 ◽  
Vol 183 (8) ◽  
pp. 1664-1673 ◽  
Author(s):  
Nobuko Ohba ◽  
Shuji Ogata ◽  
Takahisa Kouno ◽  
Tomoyuki Tamura ◽  
Ryo Kobayashi
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Real Space ◽  
Linear Scaling ◽  
Functional Theory ◽  
Space Density ◽  
Overlapping Domains

Kohn–Sham approach for fast hybrid density functional calculations in real-space numerical grid methods

2018 ◽  
Vol 230 ◽  
pp. 21-26 ◽  
Author(s):  
Jaewook Kim ◽  
Sungwoo Kang ◽  
Jaechang Lim ◽  
Sang-Yeon Hwang ◽  
Woo Youn Kim
Keyword(s):  
Density Functional Calculations ◽  
Density Functional ◽  
Real Space ◽  
Numerical Grid ◽  
Hybrid Density Functional
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