# Building Kohn–Sham Potentials for Ground and Excited States

Ontology type: schema:ScholarlyArticle      Open Access: True

### Article Info

DATE

2022-06-20

AUTHORS ABSTRACT

We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given k and a target density ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho$$\end{document}, there exist potentials having kth bound mixed states which densities are arbitrarily close to ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho$$\end{document}. The state can be chosen pure in dimension d=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=1$$\end{document} and without interactions, and we provide numerical and theoretical evidence consistently leading us to conjecture that the same pure representability result holds for d=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=2$$\end{document}, but that the set of pure-state v-representable densities is not dense for d=3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=3$$\end{document}. Finally, we present an inversion algorithm taking into account degeneracies, removing the generic blocking behavior of standard ones. More... »

PAGES

949-1003

### References to SciGraph publications

• 2019-10-03. Exact exchange-correlation potentials from ground-state electron densities in NATURE COMMUNICATIONS
• 2021-06-30. Some Properties of the Potential-to-Ground State Map in Quantum Mechanics in COMMUNICATIONS IN MATHEMATICAL PHYSICS
• 2018-09-13. Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem in MATHEMATICAL PHYSICS, ANALYSIS AND GEOMETRY
• 2000. SCF algorithms for HF electronic calculations in MATHEMATICAL MODELS AND METHODS FOR AB INITIO QUANTUM CHEMISTRY
• 1988. Nonlinear Functional Analysis and its Applications, IV: Applications to Mathematical Physics in NONE
• 1985-02. Density functional approach to quantum lattice systems in JOURNAL OF STATISTICAL PHYSICS
• 1984-03. The inverse problem in classical statistical mechanics in COMMUNICATIONS IN MATHEMATICAL PHYSICS
• 2018-06-14. The semi-classical limit of large fermionic systems in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
• 2021-11-08. Ten Years of Glory in the α-Functionalizations of Acetophenones: Progress Through Kornblum Oxidation and C–H Functionalization in TOPICS IN CURRENT CHEMISTRY
• 2011. Density Functional Theory, An Advanced Course in NONE

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00205-022-01804-1

DOI

http://dx.doi.org/10.1007/s00205-022-01804-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1148809170

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