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2020 The local density approximation in density functional theory
Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
Pure Appl. Anal. 2(1): 35-73 (2020). DOI: 10.2140/paa.2020.2.35

Abstract

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.

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Mathieu Lewin. Elliott H. Lieb. Robert Seiringer. "The local density approximation in density functional theory." Pure Appl. Anal. 2 (1) 35 - 73, 2020. https://doi.org/10.2140/paa.2020.2.35

Information

Received: 3 April 2019; Revised: 15 July 2019; Accepted: 20 August 2019; Published: 2020
First available in Project Euclid: 13 December 2019

zbMATH: 07159296
MathSciNet: MR4041277
Digital Object Identifier: 10.2140/paa.2020.2.35

Subjects:
Primary: 35Q40 , 81V55 , 82B10

Keywords: density functional theory , Schrödinger operators , statistical mechanics , uniform electron gas

Rights: Copyright © 2020 Mathematical Sciences Publishers

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