Non-periodic finite-element formulation of orbital-free density functional theory |
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Authors: | Vikram Gavini Kaushik Bhattacharya |
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Institution: | a Division of Engineering and Applied Science, California Institute of Technology, CA 91125, USA b Lawrence Livermore National Laboratory, Livermore, CA 94550, USA |
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Abstract: | 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. |
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Keywords: | Finite elements Density functional theory (DFT) Variational calculus _method=retrieve& _eid=1-s2 0-S0022509606001645& _mathId=si33 gif& _pii=S0022509606001645& _issn=00225096& _acct=C000069490& _version=1& _userid=6211566& md5=88eec7584367d4969922d73f942e4f3c')" style="cursor:pointer Γ-convergence" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">Γ-convergence |
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