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The
local density approximation in density functional theory
Mathieu Lewin, Elliott H. Lieb and Robert Seiringer |
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Vol. 2 (2020), No. 1, 35–73
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Abstract |
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We give the first mathematically rigorous justification of the local density approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy–Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the uniform electron gas energy of this density. The error involves gradient terms and justifies the use of the local density approximation in the situation where the density is very flat on sufficiently large regions in space. |
Keywords
Schrödinger operators, statistical mechanics, density
functional theory, uniform electron gas
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Mathematical Subject Classification 2010
Primary: 35Q40, 81V55, 82B10
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Milestones
Received: 3 April 2019
Revised: 15 July 2019
Accepted: 20 August 2019
Published: 9 November 2019
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Authors |
| Mathieu Lewin | |
| CNRS & CEREMADE Université Paris-Dauphine PSL University Paris France |
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| Elliott H. Lieb | |
| Departments of Mathematics and
Physics Princeton University Princeton, NJ United States |
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| Robert Seiringer | |
| Institute of Science and Technology
Austria Klosterneuburg Austria |
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