The structure of the density-potential mapping. Part I: Standard density-functional theory

Abstract

The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review aims at clarifying the status of the Hohenberg-Kohn theorem within DFT and Part II at different extensions of the theory that include magnetic fields. We collect evidence that the Hohenberg-Kohn theorem does not so much form the basis of DFT, but is rather the consequence of a more comprehensive mathematical framework. Such results are especially useful when it comes to the construction of generalized DFTs.

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Cited by in corpus (19)

• Measuring Electron Correlation. The Impact of Symmetry and Orbital Transformations
• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• The structure of the density-potential mapping. Part II: Including magnetic fields
• A Snapshot of Time-Dependent Density-Functional Theory
• Exchange energies with forces in density-functional theory
• Geometrical Perspective on Spin-Lattice Density-Functional Theory
• Geometry of Degeneracy in Potential and Density Space
• Solution of the v-representability problem on a one-dimensional torus
• Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
• Quantum-Electrodynamical Density-Functional Theory Exemplified by the Quantum Rabi Model
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• Capturing electron correlation at mean-field cost: Assessment of i-DMFT and the underlying correlation conjecture