Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Real-space density kernel method for Kohn–Sham density functional theory calculations at high temperature

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/5.0082523· OSTI ID:1866178
 [1];  [1];  [1];  [2];  [1]
  1. College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
  2. Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
+ Show Author Affiliations

Kohn–Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. In this work, we present a density matrix based method for Kohn–Sham calculations at high temperatures that eliminates the need for diagonalization entirely, thus reducing the cost of such calculations significantly. Specifically, we develop real-space expressions for the electron density, electronic free energy, Hellmann–Feynman forces, and Hellmann–Feynman stress tensor in terms of an orthonormal auxiliary orbital basis and its density kernel transform, the density kernel being the matrix representation of the density operator in the auxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, we next develop an approach akin to Clenshaw–Curtis spectral quadrature to calculate the individual columns of the density kernel based on the Fermi operator expansion in Chebyshev polynomials and employ a similar approach to evaluate band structure and entropic energy components. We implement the proposed formulation in the SPARC electronic structure code, using which we show systematic convergence of the aforementioned quantities to exact diagonalization results, and obtain significant speedups relative to conventional diagonalization based methods. Finally, we employ the new method to compute the self-diffusion coefficient and viscosity of aluminum at 116 045 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1866178
Alternate ID(s):
OSTI ID: 1847017
OSTI ID: 1867400
Report Number(s):
LLNL-JRNL-830272; 1046746
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 9 Vol. 156; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (61)

Frontiers and Challenges in Warm Dense Matter book January 2014
Order-N first-principles calculations with the conquest code journal July 2007
Spectral Quadrature method for accurate O ( N ) electronic structure calculations of metals and insulators journal March 2016
SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters journal March 2017
SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems journal July 2017
SQDFT: Spectral Quadrature method for large-scale parallel O ( N ) Kohn–Sham calculations at high temperature journal March 2018
Alternating Anderson–Richardson method: An efficient alternative to preconditioned Krylov methods for large, sparse linear systems journal January 2019
Extended first-principles molecular dynamics model for high temperature simulations in the Abinit code: Application to warm dense aluminum journal February 2022
On spectral quadrature for linear-scaling Density Functional Theory journal October 2013
Restarted Pulay mixing for efficient and robust acceleration of fixed-point iterations journal August 2015
Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations journal March 2016
On preconditioning the self-consistent field iteration in real-space Density Functional Theory journal January 2020
Large-scale molecular dynamics simulations of dense plasmas: The Cimarron Project journal March 2012
Self-consistent-field calculations using Chebyshev-filtered subspace iteration journal November 2006
A mesh-free convex approximation scheme for Kohn–Sham density functional theory journal June 2011
Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn–Sham equation journal October 2014
Augmented Lagrangian formulation of orbital-free density functional theory journal October 2014
Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems journal February 2016
Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory journal February 2016
Non-periodic finite-element formulation of Kohn–Sham density functional theory journal February 2010
SPARC: Simulation Package for Ab-initio Real-space Calculations journal July 2021
Ab Initio Molecular Dynamics book January 2009
Electronic Structure book January 2004
Development of a Multiphase Beryllium Equation of State and Physics-based Variations journal February 2021
Algorithms and novel applications based on the isokinetic ensemble. I. Biophysical and path integral molecular dynamics journal January 2003
Introducing ONETEP : Linear-scaling density functional simulations on parallel computers journal February 2005
Pulay forces from localized orbitals optimized in situ using a psinc basis set journal June 2012
Daubechies wavelets for linear scaling density functional theory journal May 2014
Extended application of Kohn-Sham first-principles molecular dynamics method with plane wave approximation at high energy—From cold materials to hot dense plasmas journal April 2016
Perspective: Methods for large-scale density functional calculations on metallic systems journal December 2016
Discrete discontinuous basis projection method for large-scale electronic structure calculations journal September 2018
On the calculation of the stress tensor in real-space Kohn-Sham density functional theory journal November 2018
Real-space formulation of the stress tensor for O(N) density functional theory: Application to high temperature calculations journal July 2020
\mathcal{O}(N) methods in electronic structure calculations journal February 2012
The SIESTA method for ab initio order- N materials simulation journal March 2002
The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science journal May 2014
Inhomogeneous Electron Gas journal November 1964
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Ab initiomolecular dynamics for liquid metals journal January 1993
Tight-binding electronic-structure calculations and tight-binding molecular dynamics with localized orbitals journal April 1995
Real-space formulation of the electrostatic potential and total energy of solids journal March 2005
Optimized norm-conserving Vanderbilt pseudopotentials journal August 2013
Efficient formalism for warm dense matter simulations journal October 2015
Stochastic density functional theory at finite temperatures journal March 2018
Equation of state of boron nitride combining computation, modeling, and experiment journal April 2019
Very-high-temperature molecular dynamics journal January 2006
Static and dynamic conductivity of warm dense matter within a density-functional approach: Application to aluminum and gold journal March 2006
Parallel self-consistent-field calculations via Chebyshev-filtered subspace acceleration journal December 2006
Ionic and electronic transport properties in dense plasmas by orbital-free density functional theory journal December 2015
Self-Averaging Stochastic Kohn-Sham Density-Functional Theory journal September 2013
Orbital-Free Density-Functional Theory Simulations of the Dynamic Structure Factor of Warm Dense Aluminum journal October 2013
Accurate and Scalable O ( N ) Algorithm for First-Principles Molecular-Dynamics Computations on Large Parallel Computers journal January 2014
Fast and Universal Kohn-Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma journal July 2020
Efficacious Form for Model Pseudopotentials journal May 1982
Efficient Linear Scaling Algorithm for Tight-Binding Molecular Dynamics journal July 1994
First-Principles Calculation of Transport Coefficients journal December 1998
Aluminum Equation-of-State Data in the Warm Dense Matter Regime journal August 2003
Linear scaling electronic structure methods journal July 1999
The Formation of Warm Dense Matter: Experimental Evidence for Electronic Bond Hardening in Gold journal February 2009
ScaLAPACK Users' Guide book January 1997
Augmented Orbital Minimization Method for Linear Scaling Electronic Structure Calculations journal March 2007

Similar Records

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY