Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T06:11:14.977Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  20 August 2015

Linda Hung ,
Chen Huang  and
Emily A. Carter
Linda Hung*
Affiliation:
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA
Chen Huang*
Affiliation:
Department of Physics, Princeton University, Princeton, NJ 08544, USA
Emily A. Carter*
Affiliation:
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA Department of Mechanical and Aerospace Engineering and Andlinger Center for Energy and the Environment, Princeton University, Princeton, NJ 08544, USA
*
Email:linda.himg@polytechnique.edu
Email:chenh@lanl.gov
Corresponding author.Email:eac@princeton.edu
Get access

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.

Keywords

65Z0574G6549M1581V99Density functional theorytruncated Newton methodconjugate gradient methodconstrained optimizationbenchmarks
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 1 , July 2012 , pp. 135 - 161
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Wang, Y. A. and Carter, E. A., in Theoretical Methods in Condensed Phase Chemistry, edited by Schwartz, S. D., (Kluwer, 2000) p. 117–184.Google Scholar
[2]Ho, G. S., Lignères, V. L., and Carter, E. A., Comput. Phys. Commun. 179, 839 (2008).Google Scholar
[3]Hung, L. and Carter, E. A., Chem. Phys. Lett. 475, 163 (2009).Google Scholar
[4]Wang, Y. A., Govind, N., and Carter, E. A., Phys. Rev. B 60, 16350 (1999).Google Scholar
[5]Huang, C. and Carter, E. A., Phys. Chem. Chem. Phys. 10, 7109 (2008).Google Scholar
[6]Hung, L., Huang, C., Shin, I., Ho, G. S., Lignères, V. L., and Carter, E. A., Comput. Phys. Commun. 181, 2208 (2010).Google Scholar
[7]Nocedal, J. and Wright, S., Numerical Optimization (New York: Springer, 2006).Google Scholar
[8]Jiang, H. and Yang, W., J. Chem. Phys. 121, 2030 (2004).Google Scholar
[9]Weizsäcker, C. F. von, Z. Phys. 96, 431 (1935).Google Scholar
[10]Lignères, V. L. E., Advances in orbital-free density-functional theory (Princeton University, United States –New Jersey, 2008).Google Scholar
[11]Wang, L. and Teter, M. P., Phys. Rev. B 45, 13196 (1992).Google Scholar
[12]García-Aldea, D. and Alvarellos, J. E., Phys. Rev. A 76, 052504 (2007).Google Scholar
[13]Huang, C. and Carter, E. A., Phys. Rev. B 81, 045206 (2010).Google Scholar
[14]Thomas, L. H., Proc. Cambridge Philos. Soc. 23, 542 (1927).CrossRefGoogle Scholar
[15]Fermi, E., Z. Phys. 48, 73 (1928).Google Scholar
[16]Lindhard, J., Dan., K.Vidensk. Selsk. Mat. -Fys. Medd. 28, 8 (1954).Google Scholar
[17]Ashcroft, N. W. and Mermin, D. N., Solid State Physics (Brooks Cole, 1976).Google Scholar
[18]Watson, S. C. and Carter, E. A., Comput. Phys. Commun. 128, 67 (2000).Google Scholar
[19]García-Cervera, C. J., Commun. Comput. Phys. 2, 334 (2007).Google Scholar
[20]Garcia-Aldea, D. and Alvarellos, J. E., Phys. Rev. A 77, 022502 (2008).Google Scholar
[21]Allen, M. P. and Tildesley, D. J., Computer Simulation of Liquids (Clarendon Press, Oxford, 1987).Google Scholar
[22]Wang, Y. A., Govind, N., and Carter, E. A., Phys. Rev. B 64, 089903 (2001).CrossRefGoogle Scholar
[23]Shin, I., Ramasubramaniam, A., Huang, C., Hung, L., and Carter, E. A., Philos. Mag. 89, 3195 (2009).CrossRefGoogle Scholar
[24]Ceperley, D. M. and Alder, B. J., Phys. Rev. Lett. 45, 566 (1980).Google Scholar
[25]Perdew, J. P. and Zunger, A., Phys. Rev. B 23, 5048 (1981).Google Scholar
[26]Hager, W. W. and Zhang, H., SIAM J. Optim. 16, 170 (2005).Google Scholar