Commun. Comput. Phys., 2 (2007), pp. 334-357.

An Efficient Real Space Method for Orbital-Free Density-Functional Theory

Carlos J. Garcia-Cervera 1*

1 Department of Mathematics, University of California, Santa Barbara, CA 93106, USA.

Received 3 July 2006; Accepted (in revised version) 9 August 2006
Communicated by Weinan E
Available online 30 September 2006


We consider the Thomas-Fermi-von Weizsacker energy functional, with the Wang-Teter correction, and present an efficient real space method for Orbital-Free Density Functional Theory. It is proved that the energy minimizer satisfies a second order quasilinear elliptic equation, even at the points where the electron density vanishes. This information is used to construct an efficient energy minimization method for the resulting constrained problem, based on the truncated Newton method for unconstrained optimization. The Wang-Teter kernel is analyzed, and its behavior in real space at short and far distances is determined. %This information is used to construct an %accurate treatment of the kernel in real space. A second order accurate discretization of the energy is obtained using finite differences. The efficiency and accuracy of the method is illustrated with numerical simulations in an Aluminium FCC lattice.

AMS subject classifications: 65M05, 74G65, 78M50

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

*Corresponding author.
Email: (C. J. Garcia-Cervera)

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