Commun. Comput. Phys., 12 (2012), pp. 135-161.


Preconditioners and Electron Density Optimization in Orbital-Free Density Functional Theory

Linda Hung 1, Chen Huang 2, Emily A. Carter 3*

1 Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA.
2 Department of Physics, Princeton University, Princeton, NJ 08544, USA.
3 Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA; and Department of Mechanical and Aerospace Engineering and Andlinger Center for Energy and the Environment, Princeton University, Princeton, NJ 08544, USA.

Received 19 January 2011; Accepted (in revised version) 9 September 2011
Available online 20 January 2012
doi:10.4208/cicp.190111.090911a

Abstract

Orbital-free density functional theory (OFDFT) is a quantum mechanical method in which the energy of a material depends only on the electron density and ionic positions. We examine some popular algorithms for optimizing the electron density distribution in OFDFT, explaining their suitability, benchmarking their performance, and suggesting some improvements. We start by describing the constrained optimization problem that encompasses electron density optimization. Next, we discuss the line search (including Wolfe conditions) and the nonlinear conjugate gradient and truncated Newton algorithms, as implemented in our open source OFDFT code. We finally focus on preconditioners derived from OFDFT energy functionals. Newly-derived preconditioners are successful for simulation cells of all sizes without regions of low electron-density and for small simulation cells with such regions.

AMS subject classifications: 65Z05, 74G65, 49M15, 81V99

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Key words: Density functional theory, truncated Newton method, conjugate gradient method, constrained optimization, benchmarks.

*Corresponding author.
Email: linda.hung@polytechnique.edu (L. Hung), chenh@lanl.gov (C. Huang), eac@princeton.edu (E. A. Carter)
 

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