Revisiting density-functional theory of the total current density.

Area of Science:

• Quantum Chemistry
• Condensed Matter Physics
• Computational Materials Science

Background:

• Density-functional theory (DFT) typically uses electron density as the sole variable.
• Incorporating magnetic fields into DFT requires an additional variable, often the total current density in time-dependent cases.
• In static ground-state DFT, the gauge-dependent paramagnetic current density has been used, posing theoretical challenges.

Purpose of the Study:

• To reinterpret and clarify Diener's proposed exact reformulation of ground-state DFT using total current density.
• To analyze the validity of Diener's unorthodox variational principle for ground-state DFT.
• To assess the correctness of Diener's Hohenberg-Kohn-like mapping for total current density.

Main Methods:

• Reinterpretation of Diener's formulation using a maximin variational principle.
• Analysis of convexity properties derived from the variational expressions.
• Mathematical proof of the limitations of Diener's approach.

Main Results:

• Diener's formulation, based on a maximin variational principle, is shown to be incapable of reproducing the correct ground-state energy.
• The proposed construction of a Hohenberg-Kohn map within Diener's framework contains an irreparable mistake.
• The gauge-dependent paramagnetic current density, not the gauge-invariant total current density, incorrectly appears as the additional variable in the static ground-state setting.

Conclusions:

• Diener's proposed exact ground-state density-functional theory reformulation using total current density is fundamentally flawed.
• The theoretical framework requires further development to accurately incorporate magnetic-field effects within DFT.
• The study highlights critical issues in existing theoretical approaches to magnetic DFT.