---
_id: '14992'
abstract:
- lang: eng
  text: In this chapter we first review the Levy–Lieb functional, which gives the
    lowest kinetic and interaction energy that can be reached with all possible quantum
    states having a given density. We discuss two possible convex generalizations
    of this functional, corresponding to using mixed canonical and grand-canonical
    states, respectively. We present some recent works about the local density approximation,
    in which the functionals get replaced by purely local functionals constructed
    using the uniform electron gas energy per unit volume. We then review the known
    upper and lower bounds on the Levy–Lieb functionals. We start with the kinetic
    energy alone, then turn to the classical interaction alone, before we are able
    to put everything together. A later section is devoted to the Hohenberg–Kohn theorem
    and the role of many-body unique continuation in its proof.
alternative_title:
- Mathematics and Molecular Modeling
article_processing_charge: No
arxiv: 1
author:
- first_name: Mathieu
  full_name: Lewin, Mathieu
  last_name: Lewin
- first_name: Elliott H.
  full_name: Lieb, Elliott H.
  last_name: Lieb
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: 'Lewin M, Lieb EH, Seiringer R. Universal Functionals in Density Functional
    Theory. In: Cances E, Friesecke G, eds. <i>Density Functional Theory</i>. 1st
    ed. MAMOMO. Springer; 2023:115-182. doi:<a href="https://doi.org/10.1007/978-3-031-22340-2_3">10.1007/978-3-031-22340-2_3</a>'
  apa: Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2023). Universal Functionals in
    Density Functional Theory. In E. Cances &#38; G. Friesecke (Eds.), <i>Density
    Functional Theory</i> (1st ed., pp. 115–182). Springer. <a href="https://doi.org/10.1007/978-3-031-22340-2_3">https://doi.org/10.1007/978-3-031-22340-2_3</a>
  chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Universal Functionals
    in Density Functional Theory.” In <i>Density Functional Theory</i>, edited by
    Eric Cances and Gero Friesecke, 1st ed., 115–82. MAMOMO. Springer, 2023. <a href="https://doi.org/10.1007/978-3-031-22340-2_3">https://doi.org/10.1007/978-3-031-22340-2_3</a>.
  ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Universal Functionals in Density
    Functional Theory,” in <i>Density Functional Theory</i>, 1st ed., E. Cances and
    G. Friesecke, Eds. Springer, 2023, pp. 115–182.
  ista: 'Lewin M, Lieb EH, Seiringer R. 2023.Universal Functionals in Density Functional
    Theory. In: Density Functional Theory. Mathematics and Molecular Modeling, , 115–182.'
  mla: Lewin, Mathieu, et al. “Universal Functionals in Density Functional Theory.”
    <i>Density Functional Theory</i>, edited by Eric Cances and Gero Friesecke, 1st
    ed., Springer, 2023, pp. 115–82, doi:<a href="https://doi.org/10.1007/978-3-031-22340-2_3">10.1007/978-3-031-22340-2_3</a>.
  short: M. Lewin, E.H. Lieb, R. Seiringer, in:, E. Cances, G. Friesecke (Eds.), Density
    Functional Theory, 1st ed., Springer, 2023, pp. 115–182.
date_created: 2024-02-14T14:44:33Z
date_published: 2023-07-19T00:00:00Z
date_updated: 2024-02-20T08:33:06Z
day: '19'
department:
- _id: RoSe
doi: 10.1007/978-3-031-22340-2_3
edition: '1'
editor:
- first_name: Eric
  full_name: Cances, Eric
  last_name: Cances
- first_name: Gero
  full_name: Friesecke, Gero
  last_name: Friesecke
external_id:
  arxiv:
  - '1912.10424'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1912.10424
month: '07'
oa: 1
oa_version: Preprint
page: 115-182
publication: Density Functional Theory
publication_identifier:
  eisbn:
  - '9783031223402'
  isbn:
  - '9783031223396'
  issn:
  - 3005-0286
publication_status: published
publisher: Springer
quality_controlled: '1'
series_title: MAMOMO
status: public
title: Universal Functionals in Density Functional Theory
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...