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On Connecting Density Functional Approximations to Theory

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Density Functional Theory

Part of the book series: Mathematics and Molecular Modeling ((MAMOMO))

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Abstract

Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by the vagueness of the argumentation for using spin densities. Questioning the foundations of density functional models leads to a search for alternative explanations. Seeing them as using models for pair densities is one of them. Another is considering density functional approximations as a way to extrapolate results obtained in a model system to those of a corresponding physical one.

Dedicated to Jean-Paul Malrieu on his 80th birthday

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Notes

  1. 1.

    For the standard Kohn–Sham model, \(\mathcal {E}(w=0)\) is a sum of orbital energies.

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Acknowledgements

Eric Cancès’ comments on the first draft on the manuscript are gratefully acknowledged.

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Authors and Affiliations

  1. Laboratoire de Chimie Théorique, CNRS and Sorbonne University, Paris, France

    Andreas Savin

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  1. Andreas Savin
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Correspondence to Andreas Savin .

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Editors and Affiliations

  1. CERMICS, Ecole des Ponts and Inria Paris, Marne-la-Vallée, France

    Eric Cancès

  2. Department of Mathematics, Technische Universität München, Garching bei München, Germany

    Gero Friesecke

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Savin, A. (2023). On Connecting Density Functional Approximations to Theory. In: Cancès, E., Friesecke, G. (eds) Density Functional Theory. Mathematics and Molecular Modeling. Springer, Cham. https://doi.org/10.1007/978-3-031-22340-2_2

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