Volume 12, Issue 1
Preconditioners and Electron Density Optimization in Orbital-Free Density Functional Theory

Linda Hung, Chen Huang & Emily A. Carter

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

Published online: 2012-12

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  • 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.

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@Article{CiCP-12-135, author = {}, title = {Preconditioners and Electron Density Optimization in Orbital-Free Density Functional Theory}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {1}, pages = {135--161}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.190111.090911a}, url = {http://global-sci.org/intro/article_detail/cicp/7287.html} }
TY - JOUR T1 - Preconditioners and Electron Density Optimization in Orbital-Free Density Functional Theory JO - Communications in Computational Physics VL - 1 SP - 135 EP - 161 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.190111.090911a UR - https://global-sci.org/intro/article_detail/cicp/7287.html KW - AB -

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.

Linda Hung, Chen Huang & Emily A. Carter. (2020). Preconditioners and Electron Density Optimization in Orbital-Free Density Functional Theory. Communications in Computational Physics. 12 (1). 135-161. doi:10.4208/cicp.190111.090911a
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