Non-periodic finite-element formulation of orbital-free density functional theory
We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real-space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.
© 2006 Elsevier Ltd. Received 15 July 2006; revised 14 September 2006; accepted 26 September 2006. Available online 28 November 2006. The financial support of the Army Research Office under MURI Grant no. DAAD19- 01-1-0517 is gratefully acknowledged. M.O. also gratefully acknowledges the support of the Department of Energy through Caltech's ASCI ASAP Center for the Simulation of the Dynamic Response of Materials. This work was performed in part under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.
Vikram Gavini, Jaroslaw Knap, Kaushik Bhattacharya, Michael Ortiz, Corrigendum to "Non-periodic finite-element formulation of orbital-free density functional theory" [Journal of the Mechanics and Physics of Solids 55 (2007) 669–696], Journal of the Mechanics and Physics of Solids, Volume 58, Issue 11, November 2010, Page 1834, ISSN 0022-5096, http://dx.doi.org/10.1016/j.jmps.2010.08.003. (http://www.sciencedirect.com/science/article/pii/S0022509610001651)