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Title: Energy window stochastic density functional theory

Abstract

Linear scaling density functional theory is important for understanding electronic structure properties of nanometer scale systems. Recently developed stochastic density functional theory can achieve linear or even sublinear scaling for various electronic properties without relying on the sparsity of the density matrix. The basic idea relies on projecting stochastic orbitals onto the occupied space by expanding the Fermi-Dirac operator and repeating this for Nχ stochastic orbitals. Often, a large number of stochastic orbitals are required to reduce the statistical fluctuations (which scale as Nχ -1/2) below a tolerable threshold. In this work, we introduce a new stochastic density functional theory that can efficiently reduce the statistical fluctuations for certain observable and can also be integrated with an embedded fragmentation scheme. The approach is based on dividing the occupied space into energy windows and projecting the stochastic orbitals with a single expansion onto all windows simultaneously. This allows for a significant reduction of the noise as illustrated for bulk silicon with a large supercell. We also provide theoretical analysis to rationalize why the noise can be reduced only for a certain class of ground state properties, such as the forces and electron density.

Authors:
 [1]; ORCiD logo [2];  [3]; ORCiD logo [4]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Hebrew Univ. of Jerusalem (Israel). Fritz Haber Center of Molecular Dynamics and Institute of Chemistry
  3. Univ. of California, Los Angeles, CA (United States)
  4. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Tel Aviv Univ., Ramat Aviv (Israel). The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1577611
Alternate Identifier(s):
OSTI ID: 1563022; OSTI ID: 1619128
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 151; Journal Issue: 11; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Chen, Ming, Baer, Roi, Neuhauser, Daniel, and Rabani, Eran. Energy window stochastic density functional theory. United States: N. p., 2019. Web. doi:10.1063/1.5114984.
Chen, Ming, Baer, Roi, Neuhauser, Daniel, & Rabani, Eran. Energy window stochastic density functional theory. United States. doi:10.1063/1.5114984.
Chen, Ming, Baer, Roi, Neuhauser, Daniel, and Rabani, Eran. Fri . "Energy window stochastic density functional theory". United States. doi:10.1063/1.5114984. https://www.osti.gov/servlets/purl/1577611.
@article{osti_1577611,
title = {Energy window stochastic density functional theory},
author = {Chen, Ming and Baer, Roi and Neuhauser, Daniel and Rabani, Eran},
abstractNote = {Linear scaling density functional theory is important for understanding electronic structure properties of nanometer scale systems. Recently developed stochastic density functional theory can achieve linear or even sublinear scaling for various electronic properties without relying on the sparsity of the density matrix. The basic idea relies on projecting stochastic orbitals onto the occupied space by expanding the Fermi-Dirac operator and repeating this for Nχ stochastic orbitals. Often, a large number of stochastic orbitals are required to reduce the statistical fluctuations (which scale as Nχ -1/2) below a tolerable threshold. In this work, we introduce a new stochastic density functional theory that can efficiently reduce the statistical fluctuations for certain observable and can also be integrated with an embedded fragmentation scheme. The approach is based on dividing the occupied space into energy windows and projecting the stochastic orbitals with a single expansion onto all windows simultaneously. This allows for a significant reduction of the noise as illustrated for bulk silicon with a large supercell. We also provide theoretical analysis to rationalize why the noise can be reduced only for a certain class of ground state properties, such as the forces and electron density.},
doi = {10.1063/1.5114984},
journal = {Journal of Chemical Physics},
number = 11,
volume = 151,
place = {United States},
year = {2019},
month = {9}
}

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Works referenced in this record:

Self-Averaging Stochastic Kohn-Sham Density-Functional Theory
journal, September 2013


Orbital formulation for electronic-structure calculations with linear system-size scaling
journal, April 1993


Overlapped embedded fragment stochastic density functional theory for covalently-bonded materials
journal, January 2019

  • Chen, Ming; Baer, Roi; Neuhauser, Daniel
  • The Journal of Chemical Physics, Vol. 150, Issue 3
  • DOI: 10.1063/1.5064472

Structure of solid-state systems from embedded-cluster calculations: A divide-and-conquer approach
journal, May 1996


Canonical purification of the density matrix in electronic-structure theory
journal, November 1998


Linear scaling electronic structure methods
journal, July 1999


Self-consistent first-principles technique with linear scaling
journal, April 1995


Computer simulation of local order in condensed phases of silicon
journal, April 1985


Performance of Kinetic Energy Functionals for Interaction Energies in a Subsystem Formulation of Density Functional Theory
journal, November 2009

  • Götz, Andreas W.; Beyhan, S. Maya; Visscher, Lucas
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 12
  • DOI: 10.1021/ct9001784

Efficient pseudopotentials for plane-wave calculations
journal, January 1991


Phonons and related crystal properties from density-functional perturbation theory
journal, July 2001

  • Baroni, Stefano; de Gironcoli, Stefano; Dal Corso, Andrea
  • Reviews of Modern Physics, Vol. 73, Issue 2
  • DOI: 10.1103/revmodphys.73.515

Low Complexity Algorithms for Electronic Structure Calculations
journal, May 1995


Communication: Embedded fragment stochastic density functional theory
journal, July 2014

  • Neuhauser, Daniel; Baer, Roi; Rabani, Eran
  • The Journal of Chemical Physics, Vol. 141, Issue 4
  • DOI: 10.1063/1.4890651

First-principles calculations for point defects in solids
journal, March 2014

  • Freysoldt, Christoph; Grabowski, Blazej; Hickel, Tilmann
  • Reviews of Modern Physics, Vol. 86, Issue 1
  • DOI: 10.1103/revmodphys.86.253

Electronic processes in fast thermite chemical reactions: A first-principles molecular dynamics study
journal, June 2008


Real-space implementation of nonlocal pseudopotentials for first-principles total-energy calculations
journal, December 1991


Embedded density functional theory for covalently bonded and strongly interacting subsystems
journal, April 2011

  • Goodpaster, Jason D.; Barnes, Taylor A.; Miller, Thomas F.
  • The Journal of Chemical Physics, Vol. 134, Issue 16
  • DOI: 10.1063/1.3582913

Propagation Methods for Quantum Molecular Dynamics
journal, October 1994


Unconstrained minimization approach for electronic computations that scales linearly with system size
journal, November 1993

  • Ordejón, Pablo; Drabold, David A.; Grumbach, Matthew P.
  • Physical Review B, Vol. 48, Issue 19
  • DOI: 10.1103/physrevb.48.14646

Self-consistently determined properties of solids without band-structure calculations
journal, October 1991


A density‐matrix divide‐and‐conquer approach for electronic structure calculations of large molecules
journal, October 1995

  • Yang, Weitao; Lee, Tai‐Sung
  • The Journal of Chemical Physics, Vol. 103, Issue 13
  • DOI: 10.1063/1.470549

Stochastic density functional theory at finite temperatures
journal, March 2018


Time-dependent quantum-mechanical methods for molecular dynamics
journal, April 1988


Atomistic simulations of complex materials: ground-state and excited-state properties
journal, March 2002

  • Frauenheim, Thomas; Seifert, Gotthard; Elstner, Marcus
  • Journal of Physics: Condensed Matter, Vol. 14, Issue 11
  • DOI: 10.1088/0953-8984/14/11/313

Efficacious Form for Model Pseudopotentials
journal, May 1982


Chebyshev expansion methods for electronic structure calculations on large molecular systems
journal, December 1997

  • Baer, Roi; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 107, Issue 23
  • DOI: 10.1063/1.474158

Frozen-Density Embedding Strategy for Multilevel Simulations of Electronic Structure
journal, April 2015

  • Wesolowski, Tomasz A.; Shedge, Sapana; Zhou, Xiuwen
  • Chemical Reviews, Vol. 115, Issue 12
  • DOI: 10.1021/cr500502v

Sparsity of the Density Matrix in Kohn-Sham Density Functional Theory and an Assessment of Linear System-Size Scaling Methods
journal, November 1997


Potential-functional embedding theory for molecules and materials
journal, November 2011

  • Huang, Chen; Carter, Emily A.
  • The Journal of Chemical Physics, Vol. 135, Issue 19
  • DOI: 10.1063/1.3659293

Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory
journal, June 2017

  • Arnon, Eitam; Rabani, Eran; Neuhauser, Daniel
  • The Journal of Chemical Physics, Vol. 146, Issue 22
  • DOI: 10.1063/1.4984931

Stochastic density functional theory
journal, April 2019

  • Fabian, Marcel D.; Shpiro, Ben; Rabani, Eran
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 9, Issue 6
  • DOI: 10.1002/wcms.1412

Inhomogeneous Electron Gas
journal, November 1964


Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965


Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms
journal, April 1996


Direct calculation of electron density in density-functional theory
journal, March 1991


Inhomogeneous Electron Gas
journal, March 1973