The Structure of Density-Potential Mapping. Part I: Standard Density-Functional Theory

The Hohenberg-Kohn theorem of density-functionaltheory(DFT) is broadly considered the conceptual basis for a full characterizationof an electronic system in its ground state by just the one-body particledensity. Part I of this review aims at clarifying the status of theHohenberg-Kohn theorem within DFT and Part II at differentextensions of the theory that include magnetic fields. We collectevidence that the Hohenberg-Kohn theorem does not so much formthe basis of DFT, but is rather the consequence of a more comprehensivemathematical framework. Such results are especially useful when itcomes to the construction of generalized DFTs.