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

Area of Science:

• Quantum Chemistry
• Condensed Matter Physics
• Computational Physics

Background:

• Density-functional theory (DFT) relies on the Hohenberg-Kohn theorem.
• The theorem posits that the ground-state properties of an electronic system are uniquely determined by its one-body particle density.

Purpose of the Study:

• To clarify the foundational status of the Hohenberg-Kohn theorem within DFT.
• To explore extensions of DFT, including those incorporating magnetic fields.

Main Methods:

• Review and analysis of the mathematical framework underpinning DFT.
• Examination of existing literature and theoretical constructs related to the Hohenberg-Kohn theorem.

Main Results:

• Evidence suggests the Hohenberg-Kohn theorem is a consequence of a more comprehensive mathematical framework, rather than its basis.
• This understanding is crucial for developing generalized DFTs.

Conclusions:

• The traditional view of the Hohenberg-Kohn theorem as the sole basis of DFT requires revision.
• A deeper mathematical framework provides a more accurate understanding of DFT and its extensions.