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Title: Stochastic density functional theory

Abstract

Linear-scaling implementations of density functional theory (DFT) reach their intended efficiency regime only when applied to systems having a physical size larger than the range of their Kohn–Sham density matrix (DM). This causes a problem since many types of large systems of interest have a rather broad DM range and are therefore not amenable to analysis using DFT methods. For this reason, the recently proposed stochastic DFT (sDFT), avoiding exhaustive DM evaluations, is emerging as an attractive alternative linear-scaling approach. This review develops a general formulation of sDFT in terms of a (non)orthogonal basis representation and offers an analysis of the statistical errors (SEs) involved in the calculation. Using a new Gaussian-type basis-set implementation of sDFT, applied to water clusters and silicon nanocrystals, it demonstrates and explains how the standard deviation and the bias depend on the sampling rate and the system size in various types of calculations. We also develop a basis-set embedded-fragments theory, demonstrating its utility for reducing the SEs for energy, density of states and nuclear force calculations. Finally, we discuss the algorithmic complexity of sDFT, showing it has CPU wall-time linear-scaling. Lastly, the method parallelizes well over distributed processors with good scalability and therefore may findmore » use in the upcoming exascale computing architectures.« less

Authors:
 [1];  [1];  [2];  [3];  [1]
  1. Hebrew Univ. of Jerusalem, Jerusalem (Israel). Fritz Haber Center for Molecular Dynamics and Inst. of Chemistry
  2. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division
  3. Univ. of California, Los Angeles, CA (United States). Dept. of Chemistry and Biochemistry
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)
OSTI Identifier:
1571134
Alternate Identifier(s):
OSTI ID: 1507443
Grant/Contract Number:  
AC02-05CH11231; DMR-1611382
Resource Type:
Accepted Manuscript
Journal Name:
Wiley Interdisciplinary Reviews: Computational Molecular Science
Additional Journal Information:
Journal Volume: 9; Journal Issue: 6; Journal ID: ISSN 1759-0876
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; density functional theory; linear scaling; stochastic methods

Citation Formats

Fabian, Marcel D., Shpiro, Ben, Rabani, Eran, Neuhauser, Daniel, and Baer, Roi. Stochastic density functional theory. United States: N. p., 2019. Web. doi:10.1002/wcms.1412.
Fabian, Marcel D., Shpiro, Ben, Rabani, Eran, Neuhauser, Daniel, & Baer, Roi. Stochastic density functional theory. United States. doi:10.1002/wcms.1412.
Fabian, Marcel D., Shpiro, Ben, Rabani, Eran, Neuhauser, Daniel, and Baer, Roi. Wed . "Stochastic density functional theory". United States. doi:10.1002/wcms.1412.
@article{osti_1571134,
title = {Stochastic density functional theory},
author = {Fabian, Marcel D. and Shpiro, Ben and Rabani, Eran and Neuhauser, Daniel and Baer, Roi},
abstractNote = {Linear-scaling implementations of density functional theory (DFT) reach their intended efficiency regime only when applied to systems having a physical size larger than the range of their Kohn–Sham density matrix (DM). This causes a problem since many types of large systems of interest have a rather broad DM range and are therefore not amenable to analysis using DFT methods. For this reason, the recently proposed stochastic DFT (sDFT), avoiding exhaustive DM evaluations, is emerging as an attractive alternative linear-scaling approach. This review develops a general formulation of sDFT in terms of a (non)orthogonal basis representation and offers an analysis of the statistical errors (SEs) involved in the calculation. Using a new Gaussian-type basis-set implementation of sDFT, applied to water clusters and silicon nanocrystals, it demonstrates and explains how the standard deviation and the bias depend on the sampling rate and the system size in various types of calculations. We also develop a basis-set embedded-fragments theory, demonstrating its utility for reducing the SEs for energy, density of states and nuclear force calculations. Finally, we discuss the algorithmic complexity of sDFT, showing it has CPU wall-time linear-scaling. Lastly, the method parallelizes well over distributed processors with good scalability and therefore may find use in the upcoming exascale computing architectures.},
doi = {10.1002/wcms.1412},
journal = {Wiley Interdisciplinary Reviews: Computational Molecular Science},
number = 6,
volume = 9,
place = {United States},
year = {2019},
month = {4}
}

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