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Title: Energy window stochastic density functional theory

Journal Article · · Journal of Chemical Physics
DOI: https://doi.org/10.1063/1.5114984 · OSTI ID:1577611
 [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
+ Show Author Affiliations

We report that 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 N$$-1/2\atop{χ}$$) 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. Finally, 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.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1577611
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 11 Vol. 151; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (37)

Stochastic density functional theory journal April 2019
Low Complexity Algorithms for Electronic Structure Calculations journal May 1995
Frozen-Density Embedding Strategy for Multilevel Simulations of Electronic Structure journal April 2015
Performance of Kinetic Energy Functionals for Interaction Energies in a Subsystem Formulation of Density Functional Theory journal November 2009
Time-dependent quantum-mechanical methods for molecular dynamics journal April 1988
Embedded density functional theory for covalently bonded and strongly interacting subsystems journal April 2011
Potential-functional embedding theory for molecules and materials journal November 2011
A density‐matrix divide‐and‐conquer approach for electronic structure calculations of large molecules journal October 1995
Chebyshev expansion methods for electronic structure calculations on large molecular systems journal December 1997
Communication: Embedded fragment stochastic density functional theory journal July 2014
Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory journal June 2017
Overlapped embedded fragment stochastic density functional theory for covalently-bonded materials journal January 2019
Atomistic simulations of complex materials: ground-state and excited-state properties journal March 2002
Inhomogeneous Electron Gas journal November 1964
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Computer simulation of local order in condensed phases of silicon journal April 1985
Efficient pseudopotentials for plane-wave calculations journal January 1991
Real-space implementation of nonlocal pseudopotentials for first-principles total-energy calculations journal December 1991
Self-consistently determined properties of solids without band-structure calculations journal October 1991
Orbital formulation for electronic-structure calculations with linear system-size scaling journal April 1993
Unconstrained minimization approach for electronic computations that scales linearly with system size journal November 1993
Self-consistent first-principles technique with linear scaling journal April 1995
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
Inhomogeneous Electron Gas journal March 1973
Stochastic density functional theory at finite temperatures journal March 2018
Electronic processes in fast thermite chemical reactions: A first-principles molecular dynamics study journal June 2008
Self-Averaging Stochastic Kohn-Sham Density-Functional Theory journal September 2013
Efficacious Form for Model Pseudopotentials journal May 1982
Direct calculation of electron density in density-functional theory journal March 1991
Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms journal April 1996
Sparsity of the Density Matrix in Kohn-Sham Density Functional Theory and an Assessment of Linear System-Size Scaling Methods journal November 1997
Linear scaling electronic structure methods journal July 1999
Phonons and related crystal properties from density-functional perturbation theory journal July 2001
First-principles calculations for point defects in solids journal March 2014
Propagation Methods for Quantum Molecular Dynamics journal October 1994
Embedded density functional theory for covalently bonded and strongly interacting subsystems text January 2011

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