The Structure of the Density-Potential Mapping. Part II: Including Magnetic Fields

Area of Science:

• Quantum mechanics
• Computational chemistry
• Condensed matter physics

Background:

• The Hohenberg-Kohn theorem establishes ground-state electronic properties using particle density in DFT.
• Extensions of DFT, particularly those including magnetic fields, require re-evaluation of this theorem.

Purpose of the Study:

• To clarify the validity of the Hohenberg-Kohn theorem in various DFT extensions.
• To analyze current-density-functional theory (CDFT) formulations and their relationship to standard DFT.
• To explore insights from Maxwell-Schrödinger DFT and quantum-electrodynamic DFT.

Main Methods:

• Review of existing literature on density-functional theory and its extensions.
• Analysis of counterexamples to the Hohenberg-Kohn theorem in paramagnetic CDFT.
• Discussion of Moreau-Yosida regularization for density functionals.

Main Results:

• The Hohenberg-Kohn theorem is not universally valid in all DFT extensions, notably in paramagnetic CDFT.
• Paramagnetic CDFT shares mathematical similarities with standard DFT.
• Moreau-Yosida regularization can address non-differentiability issues in density functionals.

Conclusions:

• The status of the Hohenberg-Kohn theorem varies across DFT extensions.
• Paramagnetic CDFT, despite limitations, offers a viable framework for electronic structure calculations.
• Further insights into magnetic field effects can be gained from Maxwell-Schrödinger and quantum-electrodynamic DFT frameworks.